The goal you need to reach to unlock this achievement is finish the game as Grolla in 60 minutes (an hour) or less.

You can start the game either by starting from the Prologue Stage, or directly going to the Stage Select. It would be better skip the prologue since it will only waste some of your time; you can still unlock the achievement even if you start from the Stage Select.
Also, make sure you play on Arcade Mode. The game's replay system records cutscenes, what probably means that you would be wasting time if you "follow" the story.

With that said, let's move to the first actual stage I recommend facing...

Yeah, this stage is the stage of quick lasers. I recommend going to this stage first because here you can get two Cross Tanks (believe me, while doing this run, the more Cross Tanks the better). There's not much to say about Freudia's stage, just make sure you don't slide on walls, otherwise, a beam might hit you and you will lose time, and go through the upper route at the last section of the stage (Grolla's dash makes it possible even if she can't get Sichte's power). Oh yeah, and collect as many lives as possible, as it will be harder for you to get a Game Over and have to restart a stage from the beginning.

I don't have any tips about Freudia's boss fight, though. Just make sure you don't lose lives.

About Liebea's stage, simply rush the stage. When climbing the left ladder, don't be afraid and ignore the fact that there's electricity placed to make you fall. Once you move to the next section, quickly dash jump to the platform at your right, then dash jump again to the platform with another ladder. The chances of you getting hit by the upper electricity is minimal due to its timing, but be careful about the middle one.

After that, you will face this section:



As you can see, these obstacles can be easily ignored just by using the Wall Jump. Later on, dash jump to the upper platforms and do it again so you can hold the ladder at top of the screen, making you instantly move to the next section. When you move to the other section, keep climbing the ladder and then quickly dash jump left to evade the enemy attack, and go to the platform leading you back to the inside. When back to the inside, you will see this section:



Stand near to the crushers to make them fall. The chains inflict no damage, so you can simply go dash jumping through them. Keep doing that until you see a mettaur-like enemy. Jump over it, and don't try to kill it. The crusher in front of you will fall and the enemy will be far enough to not be a problem. Jump over the crusher and dash to prevent the other crusher from falling onto you.



Here you can jump on the wall and go to the ladder above by Wall Jumping. After climbing, repeatedly press the Jump button to make Grolla reach faster the top of the ladder, instead of keep climbing on it.
After climbing the another ladder, Wall Jump the right wall and go to the platform with a gebyoall-like enemy and instantly dash jump to the platform with a ladder. Climb it to move to the next section and do the same as I said on the previous paragraph but pressing left, otherwise you might end up hitting a crusher in the middle of the Wall Jump (be careful to not press left too much, or you will hit the crusher, too).

After passing through the section with moving up blocks trying to smash you on the ceiling, you will be at the last section of the stage before getting past the boss shutter. Dash jump to the platform with a statue. When the statue jumps, immediately dash under it.

That's it for Liebea's stage, everything you have to do now is ignore the electricities like you did at the beginning of the stage and face her. I believe this fight won't be a problem.

At Luste's stage, go dashing until you find a skull that acts as a flamethrower. Take damage from it and destroy it. You should do that because right after will appear a fan-like enemy trying to push you back with its wind, and to "ignore" this enemy, it would be good stay in a safe ground. After you destroy the skull, dash jump to the wall above you and then wall dash jump to the other side. Things should turn out like this:



I felt insecure about reaching the other side using this method, and that's way the image shows Grolla going left. If you are high enough, you will be able to perform what I'm saying without any problems (like I would if I didn't hesitate).
After that, in another section, ignore the way the game says you to go and climb to the exit of the section by using wall jump (like you've done sometimes at Liebea's stage). Then, dash jump and attack the enemy bird before it drops its egg. After that, jump over the other fan-like enemy and do it again later (the gebyoall-like enemy won't be a problem).
In the next section there will be a Cross Tank; you probably know how to get it. By taking the Cross Tank, you won't be able to move back directly to the platforming section, you will need to fall and wall jump your way back (don't use the ladder). After passing through the platforming challenge, you will climb a ladder and move to the next section where you can collect a live. Destroying the flamethrower skull can be tricky with Grolla, but once you do, that 1-up will be already yours. If you run out of platforms (the ones that fall), it's no problem, if you time correctly your dash jump to reach the moving platform when it reaches its minimum altitude, you will be ok.

After all this, keep going through the stage normally until you reach this section:



These two platforms circle the flamethrower. You can ignore this enemy by passing under it (be aware to jump when the platforms pass through each other).
After getting past this section, there will be a fan enemy on a platform coming close to you. Hit it with a charged slash, and then dash and attack it. It's a dangerous move, but it's worth trying to master it; better than await the enemy come close to you three times.
There are no more tips I can say about rushing this stage, you already are at the end of it. Make sure you don't fall, and when you reach the solid platform that's about to come, dash along it and prepare yourself to face the boss.

The boss, though, I can give you a tip. Try getting close to Luste and attack her with a normal slash. She'll probably jump to the other side of the arena. Hurry and attack her again (normal slash, again). Keep doing it until she goes to her Desperation Mode. Keep attacking her the way you did until now, but be careful to not get hit by the charged Lustatem shots. If Grolla gets low on life, she will automatically attack with a charged slash. That will make Luste stop jumping from side to side of the arena and attack with her normal Lustatem shots to six (or eight, I don't remember now) directions. Don't panic and try to force her to get locked in a pattern as you did before.

Zorne's stage is probably as easy to rush as Liebea's, maybe even easier. The secret to rush this stage is jump over enemies, dash under shield attacker-like enemies somewhat above the ground (the ones not offering an opening to do so, jump over them) and hit that lizard-like enemies with a charged slash (their jump distance is low, what makes dashing under them a hard thing to do). It would be good using wall jumps whenever you can to make things a little bit faster, but nothing really mandatory.

About the boss fight, it should be easier beating Zorne playing as Grolla rather than playing as Spiritia for the fact that Grolla can do Wall Jump. Be careful when she gets on Desperation Mode, though, the explosion lines are bigger and probably will hit you if you don't take care.

At Schwer-Muta's stage, you can grab the Cross Tank placed for trolling purposes thanks to Grolla's dash and wall jump abilities (although you can collect it as Spiritia too, if you slide and jump at the exact moment). On the next section, rush it without too much worries.



When you reach this section, destroy the cross and dash under the wall through the "?" blocks. Quickly wall jump to ther upper part of the screen and keep dashing right until you stand on the smile blocks. When they fall, keep dashing right (Grolla, when dashing, is fast enough to not fall down at the spikes because of the "?" blocks. But if you feel uneasy about she stop dashing right above one of these blocks, feel free to jump).

After passing through the Metal Man stage reference (about it, pick up that Cross Tank) you will see this section:



It's safe picking up that 1-up as Grolla thanks to her Wall Jump; once you pick it up, get out of there.
After passing through this section, you are basically at the end of the stage. Knowing that you can pass through the "?" blocks, you might already know what to do on the next section.

Schwer's fight is simple, just fight her as the game wants you to.

Once you start Trauare's stage, proceed the stage from the upper route so you can get the 1-up at the far right of the section. Then, be careful with the spikes. After passing through the spike fall section, go through the lower path (there are too many spikes at the upper path, and it's not like you will lose too much time going under). Jump to the ladder, ignoring the snake dispenser. In the next section, ignore the mettaur-like enemy and hold at the ladder at the top of the screen for an immediate screen transition.



When you have to face the mini-boss, destroy the first two heads of it, then use the body of the tallest head to destroy the mini-boss's weak spot. If you take damage during the process, it's fine, if it is not too much.
Later on, you might think I'd recommend you going down because there's an easy-to-get life there, but, by going there, that means you are about to take high risks of you losing a life, too. It could be somewhat worthy trying it if you were playing this game normally, but losing a life means losing time, and that's something you don't want to lose if you want to unlock the achievement. So, take the upper route, it's safer.



After rushing the stage for a while, you will have to face another mini-boss. The only difference is that the water level is lower now, and there's a platform moving horizontally (this platform is useless when playing as Grolla). Do the same strategy as the previous mini-boss, but be aware of the water level.

You are about to get near to the end of the stage. Ignore the enemies at the next section, and rush the stage. If you are low on health, feel free to pick up the energy restorer located at the final section of the stage:



Trauare's boss fight can be easily broken just by wall sliding and attacking her with timed charged slashes. Keep doing that until her vitality depletes completely.

Grolla's stage is not a difficult stage to rush. At the first part of the stage, keep dashing and jumping (or attacking) whenever necessary until you see the moving platforms above a bottomless pit. Dash jump to the second platform and then dash jump over the enemy that tried to hit you with his projectiles. Then, destroy the snake dispenser so you can deal against the other enemy that'll try to shoot at you. After you destroy this enemy, charge your slash and await at the second platform so the enemy skull won't hit you. After it fires, go and release the attack and keep moving.



When you get here, wall jump this wall. Then, carefully move forward to not get hit by the enemies and their projectiles. After passing through this challenge, you will be at the mini-boss screen. This mini-boss is easy to defeat, just do as you would if playing normally this stage. When you defeat it, dash jump to the edge of the screen, the mini-boss won't damage you while blowing up.
For the next part, you can recklessly move forward, or being careful and trying to avoid damage. Just do it fast, and don't fall.

When at the underground section, go fast, but with caution. Platforming challenge here is somewhat dangerous to act recklessly, and you surely wouldn't want to lose a life that easily. Once you get past this section, you practically made it through this stage. Everything left is the fight against Spiritia.

The fight against her can be tricky. I don't have many tips about this fight, but try to keep a distance of her while trying to attack her. If she comes too close, wall dash jump to the other side, and repeat.
When she uses her Cross Tank (also, when she gets to her Desperation Mode), she will try to use Freudenstachel if you are on the ground, or close enough to it. If you are too high for her to attack you using this power, she'll switch to Lustatem. She'll use this power while coming close to you from the ground. When she gets close enough, she'll use a charged Klageharnisch. That's your chance to attack her. Keep avoiding her attacks and stay on the wall. When she threaten to use a charged Klageharnisch, get out of the wall and attack her. If she's about to lose (2 life points), then attack her again. Note that you must only use charged attacks if you don't want to take damage.

At Sichte's stage, make sure to go by the upper path when you arrive at the third screen. You can easily get a live by doing so. After that, just rush the stage (if you received some damage, feel free to go for the big vitality restorer, and other small vitality restorers if necessary).
At the first section with water flows and small waterfalls, you will see a Cross Tank. Unfortunately, you won't be able do get it as Grolla.

After beating the mini-boss at the following section, you can go to a secret room by dashing under the wall. There you can get a live and a Cross Tank. Again, don't waste time climbing ladders when you can wall jump to go faster.

When you arrive at this point...



... go dash jumping on these platforms as fast as you can, but be careful to not end up slipping. After that, you will be at the final section of the stage. Pass through it normally and you'll do fine.

I actually don't have tips about beating Sichte... At the first part of the fight, try jumping over her when you feel that she will stop walking to attack you. When she gets at her Desperation Mode... This is when I "try" to avoid her attacks while trying to hit her. This fight will probably take away from you one Cross Tank (at least, for me, that was the case).

Zeppelin Stage 1

Ok, now here is when things start to get interesting.

At the beginning of Zeppelin Stage 1, there's an easy-to-get Cross Tank at top of a wall. Collect it, and then rush the stage. If you can use wall jump instead of climbing ladders, use it, for all the stages about to come.



When you arrive at the Cossack Stage 1 reference, climb the ladder, then dash to the snake dispenser and hit with a charged slash. It won't be enough to destroy it, so attack it again with a normal slash. This is faster than having to face directly the ladder challenge and is faster than having to spam normal slashes to prevent the snakes from hitting you.

Now, you will have to face the Demon's Wall boss... Be sure to be full on health for this one, because the easiest way to beat this boss is taking damage from its attacks and use charged attacks so you can inflict damage on it. If you do things with extreme efficiency, then at least two Cross Tanks will be sacrificed for the sake of you not going nuts trying to beat it as it should be.

If things happen as I'm saying here, then you should have 4 Cross Tanks now.

Zeppelin Stage 2



At the beginning of Zeppelin Stage 2, there's a Cross Tank you can easily get. Normally, you would turn around after picking it up. Instead of that, keep going right and you will hit the lateral of a block. Once you do, immediately wall jump this block and keep rushing the stage.
Don't bother to attack enemies unless it becomes necessary.

This stage is short, so you are near to get to the boss arena.

The battle against Poltergeist is not that complicated. As Grolla, it's somewhat easier, if you pay attention to its movements, because of the Wall Jump. When you start to realize that the boss is speeding up, use wall jumps for better chances of avoiding it from hitting you.
At the last part of the battle, hit it with a charged slash and then strike it with a slash combo to finish it up quickly.
You may use a Cross Tank if you get hit too much by the boss, but it's possible beating it without using any.

Zeppelin Stage 3

About Zeppelin Stage 3, I don't have much to say. Just make sure to pick up the Cross Tank and the 1-up on this stage, and be careful to not let enemies hit you if you are at the edge of a platform or in the middle of a jump right above a bottomless pit.
When at this section...



... don't charge your slash. Slash dash through the enemies so you keep your speed.

About the fight against Raimund, you should understand his attack pattern while using the scythe. Thanks to Grolla's dash it should be easier to avoid it rather than it would be if playing as Spiritia. Make sure you beat the scythe without using Cross Tanks (Demon's Wall is not the only problem about it). If you are about to lose a life, use the Cross Tank. The fight against Raimund himself is quite easy, but don't underestimate it, as the attacks cause a lot of damage.

Zeppelin Stage 4

When the stage is about to split up in two paths, go through the upper path. Just attack enemies when necessary and keep rushing the stage.
Once you arrive at the point where the paths converge, go by the lower route. There are less enemies there, and the platforming challenge isn't so hard.
After this, you will be at the end of the stage.

The fight against the Count is somewaht easy, and there aren't any tips I can give so you can beat him faster than the normal.
Things can get dangerous at his Desperation Mode, though, so it's possible that you'll need to use a Cross Tank for this fight. However, it is pretty much possible that it won't be necessary.

After all this, now you are about to face the real final stages of the game. You are almost there!

Iris Stage 1

At the beginning of the stage, move up by the right path. After climbing the second ladder you will need to, rush the stage. When getting here...



... fall down by the left. On the next screen, don't bother awaiting for the yoku blocks to spawn, dash left and stick on the wall, then press right so you don't fall on the spikes. By doing this, you will get a Cross Tank after dashing under the wall.



At this section, dash jump and destroy the enemies before they drop the electric balls. Then, at the next section, focus on staying at the upper route. (Be careful about the last enemy that drops electric balls, you won't be able to jump over it; you'll have to destroy it.)



After rushing three screens, you will reach this part of the stage. Instead of using the yoku blocks to proceed, dash jump to the first solid block, then stabilize your footing and then dash jump to the other solid block and pass through this challenge. After this, you will face the first boss of Iris' stages.

I don't have tips about the fight against Webmaster Spider. At least this fight is easier than Bospider's from Mega Man X, so it's pretty much possible you won't need to use a Cross Tank here.

Iris Stage 2

Iris Stage 2 is technically the real final stage of the game. After this stage, is Iris Stage 3, that is a stage for boss rush, and then Iris Stage 4, that is a stage for the final battle.
That means if you pass through this stage as whole without many problems, then your "achivement unlocked" is not so far away.

For this stage, whenever you can ignore enemies (specially the ones with shielding), do it. If you see any 1-up or Cross Tank, pick it up. This isn't a hard stage to rush in the end.
The real problem lies at the end of it. Yeah, the Deviled Egg.

As Grolla doesn't get weapons, this boss can be a major problem for your run. If you use Cross Tanks here, you probably won't have enough for the upcoming challenges (it's ok to use one, I think). So, it's better train this boss's pattern without using Cross Tanks before you start this whole run. Don't do the same mistake as I did.

Iris Stage 3

If you managed to get past the Deviled Egg without using a Cross Tank (or if you used only one), then you already passed through all the worst that could ruin your run. Try not failing now after getting this far.

Rush the stage until you get to the boss teleporters.
First, beat Sichte (this can cost you a Cross Tank). Thanks for the fact that all the boss arenas have walls, you can use for your favor. If you used a Cross Tank, then you should have 6 now.
Next, beat Spiritia. Same strategy as I told before applies here.
Then, fight Luste. Same strategy, but the only difference is that the ground is flat, so be careful.
After beating her, fight against Freudia. Her "all out" attack can be a problem because the arena is smaller, but at least the attack ends sooner.
After that, fight Liebea (just to replenish your health in case you didn't go well against Freudia).
Later on, fight Traure, Zorne and Schwer, the order you prefer. Same strategy as before.

Everything left is Iris, now. Pay attention to her attacks and don't attack when you shouldn't. Being defensive now is more of a matter than being offensive. A tip: charge your slashes.
If you are efficient on this fight, you may use only one Cross Tank. You should have 5 Cross Tanks now.

Iris Stage 4

At last, the final stage. Act fast and reach the dragon, quickly free him. During the process you will get a 1-up and a Cross Tank (6 Cross Tanks, now).

The fight against Iris herself, I'd recommend training a bit (that's one of the reasons why I gave attention about collecting lives, too). Understand her attack patterns on both phases of the fight. After doing so, fight for real now, using the Cross Tanks you gathered and kept throughout the game. Fight well, and your achievement will be finally unlocked.

Losing one live or another doesn't ruin your run. I lost about 5 lives and I still beat the game with 7 lives in a time of 49 minutes and 25 seconds. Just be careful about deciding when using the Cross Tanks. If you follow my notes and tips, then you probably will be able to unlock the achievement without much problems.
It's a difficult task, and probably you will have to start over sometimes, but then again, that's what makes this achievement an achievement. Just keep trying and don't give up.

I've recorded the replay of me trying to get the achievement. Most, or, perhaps, the entirety of what I've written here can be seen in practice on this video: