DISCLAIMER: This guide contains public knowledge. You MAY use it in whatever way you want as long as you don't monetize it. You don't have to ask for permission to use any parts of it, and you don't have to give me credit, but feel free to do so.

This guide was created to help you unlock all achievement in the least possible number of playthroughs, and warn you of missable achievements, but without spoiling stuff for you.

IMPORTANT

Squid Savior is very easy to miss. If you want to unlock it on your first playthrough, make sure you don't melt ANY of the Heart Squids you collect.

PLAYTHROUGHS

You need at least 2 playthroughs to unlock all achievements, one of which would be an insanely perfect speedrun dependent on bugs (I'm not even sure if it's humanly possible without the exploits, but it is in theory). The recommended strategy is to have at least 1 normal playthrough + 2 speedruns (total of 3, or 2.5, if you branch one speedrun from the other), although you might add a leisurely playthrough before those 3 for a total of 4. Here's the plan.

Playthrough # 0 (optional): Play at your own pace and don't worry too much. I recommend going for all Collection achievements, maybe also all from "Optional (obtain at any time)". Apart from that, I'd recommend getting at least What an eyesore... and Pest Control from the "Missable (limited timeframe)" section, but it's not necessary. If you chose this path, you can even use Pirate Mode (ie, you start with all gear) to progress faster on playthrough #1.

Playthrough # 1: If you skipped "playthrough # 0", make sure you get all achievements listed above. Don't melt any Squid Heart. Since you'll have only 2 hearts for health, you might as well get all "Defeat <boss name> without taking damage" achievements. Make sure you get 100%, including 32 Heart Squids, 20 Dark Magic, and all weapon upgrades and skills from the shop.

Playthrough # 2 (speedrun): Go for Speed Runner. Read more at the "Speed Runs" section.

Playthrough # 3 (speedrun): Go for Purple Haired Warrior Maiden. Read more at the "Speed Runs" section. Note that you could branch this run from the previous run at some point. If you manage to beat the game in less than 2 hours, the extra 1.5 hour should be plenty to backtrack for anything you might have missed.

Important Note: These achievements are all one-time opportunities. Once the timeframe is past, you won't be able to unlock them. They're listed in chronological order so you don't miss them. As for beating bosses without taking damage, if you're having trouble, a general hint is farming some gems and buying upgrades from the shop, as well as items like (Super) Pike Balls and (Super) Monster Milk.

From my hair to his derriere!
Defeated the Ammo Baron without taking any damage.


How: Self-explanatory. You just need to know that the area on the floor where the crates are is a safe spot (not on top of the crates, though).


What an eyesore...
Defeated the Cyclops Plant using only Pike Balls.


How: Don't hit it in any other way. Make sure you have at least 2 or 3 Pike Balls before entering the battle, and don't be afraid to use healing items (you should load the savegame recorded right before the boss battle after getting this). For the first part, you don't need to activate the plants, just jump to hit the eye with the Pike Balls. On the second stage, follow it around and take advantage of the time when it's using the laser. Don't be afraid of taking damage. With healing items, it should be easy.


Master Gardener
Defeated the Cyclops Plant without taking damage.


How: Self-explanatory. For the first stage, hit it only with the Pistol. On the second part,
stay on one corner firing your pistol. If you see it'll land close to use, just attack like crazy with your hair. Otherwise, quickly move across the area and carefully jump over the boss to avoid the laser.


Zombie Survival Guide
Get Rottytops to Abner Tree without making any mistakes in a single attempt.


Where and when: Spiderweb Island, when you're carrying Rottytops after saving her.
How: This is hard because this section is long and you can't make any mistakes. If you die, you have to load your savefile and start over, but you're better off making it to the end a few times in order to practice. Note that, if you succeed through the hard part, you CAN save at the screen right after it, just so you don't accidentally die at the Cacklebat. If you need a video to help you, check the link below.
Video guide (the video is not mine)

Pest Control
Destroy 10 Spider Eggs before they hatch.


Where: Boss fight against Empress Spider on Spiderweb Island
How: Self-explanatory. Just wait for her to drop the eggs. Don't be afraid of taking damage or wasting healing items. Just load the game afterwards.


Squashed Spider
Defeated the Empress Spider without taking damage.


How: Self-explanatory. She has 3 attacks:
1) A series of 3 dives. Take this chance to hit her with your hair. Use Milk or Super Milk for extra damage. Using Pike Ball is not a good idea because she'll go back up faster.
2) She'll drop 2 eggs (4, after she takes damage) which will turn into spiders if you let them. When I fought her, one shot with the Pistol took care of them (my Pistol was maxed, not sure if it's needed). Careful with the dive attack after the last spawn.
3) Fire. After a second or two, the fire will spread across the whole area. Wait until the last moment to jump and glide with your Hat.
Also note that she becomes faster after she's taken some damage.


Calamari Connoisseur
Defeated the Squid Baron without taking damage.


How: Self-explanatory. Tips:
Try to stay close to the left wall and use Super Monster Milk + Super Pike Ball. When it's spinning around, shoot it if you have the chance, but don't risk getting hit for it. Use the hat to jump and let it bounce off the wall you're close to. If it stops near you, hit hard! Don't try to shoot it during the stomp + yellow wave attacks, and jump over the yellow waves without using the hat (except maybe for the third, larger wave).
If it starts eating, get near and hit it hard. As I was attempting this achievement, it always died when it was trying to eat for the first time...
... Or did it!? Now for Squid 2.0! It's basically the same pattern, only faster and harder. Also,
you need to use the Scimitar in order to break the armor. You should start
by waiting on the right and breaking the armor on the first chance you get (only when it's spinning around, NOT when it's stomping), but DON'T start hitting immediately with your hair. Instead, wait for opportunities like before, only you'll be hardly firing your Pistol this time, if at all. It'll probably rebuild its armor before it starts eating, in which case you should break it again when it's spinning around. When it finally starts eating, attack with all you've got and you should win on that first meal.
Always remember to use more Super Milk + Super Pike as soon as they expire. (Although I only used one of each when I got this achievement, don't be afraid to waste items.)


Prefectionist
Defeated Dagron without taking damage.


How: Self-explanatory. Tips:
It seems crazy hard at first, but it's actually very easy. As soon as you have control, use a Super Milk and run/dash to the right to hit the eye on the left and create platforms. Sometimes he'll destroy a platform as soon as it drops, but you'll have 2 left. Usually, he'll destroy another 1 on the other go. Anyway, move on top of one of them and hit the Dagron on the head as it flies past you. Super Spike Ball also helps. When it drops to the ground, hit it like crazy. As soon as it starts flying, run and dash to hit the furthest eye again. Repeat the process, dropping it to the ground, and it should die on the second time you do it.
If there are no platforms, he'll use the flame attack. Make sure you're on the furthest side from where he's coming to avoid that, or, if you're fast enough to dash, take advantage of the invincibility.


Fool me once…
Play keep away with the Ammo Baron.


Timeframe: Right after you get the Targeting Module, before you give it to Ammo Baron.
How: When you talk to him, pick the option "Sure... Yoink!" twice and the achievement should pop.


Scrap Metal
Defeated the Steel Maggot without taking damage.


How: Self-explanatory. Tips:
Even easier than the previous boss. As soon as you gain control, use Bubble Shield, Super Milk and Super Pike. Use the cannon to hit the three red button on its back (for me, it seems that the first button must be hit by a pike ball, but I can't be sure). As soon as you hit the last one, fall close to his tail and hit hard. Keep close to it so the Pike Balls keep it close as well. It should die on the first sequence of hits on its tail.

Nothing but a shade…
Defeated the Pirate Master without taking damage.


How: This refers to the 1st phase of the final boss (or the only phase, if you didn't get all Dark Magic). Other than that, it's self-explanatory. Tips:
It's easy. As soon as he disappears, use Super Milk, Super Pike, and Bubble, which will protect you against all his attacks (just don't touch him). Follow him around and attack repeatedly.
When he goes on top of the bone platforms, don't try to follow him up there, since you might end up being hit. Instead, carefully hit him with Pike (or double jump from a distance and shoot). Once he's back down, go back to attacing him with your hair.
If your items ever wear off, make sure you use them again.

Guardian Genie
Defeat the Pirate Master's true form.


How: To fight the final boss' true form, you need to have collected all 20 Dark Magic.

Half-Genie Hero
Defeated the Pirate Master's true form without taking any damage.


How: Oh, boy. I hope you're ready for this. Make you sure you bring 9x Super Monster Milk, 9x Super Pike Ball, and 9x Bubble Shield.
This boss has 4 phases. Phase 1 is just like the normal form you fight if you don't collect all Dark Magic. Refer to Nothing but a shade… above for tips.

Phase 2 and 3 are similar, only phase 3 is harder. I'll describe them as a single phase and point the differences. Note that you don't have your Pirate Gear with you anymore, so beware!. Also, to move from phase 2 to 3, you have to pick any option when prompted, and then dance with the LAMP button to suck the magic back in. Also, you don't need Super Milk on phase 3.
Cannonballs: Stay close to the middle, a bit to the left of where the first cannon ball from the right drops for the first time. As soon as the first ball goes up in the air, run to the RIGHT and don't stop. Backdashing (SCIMITAR button, and I'm assuming you bought that skill) also works, but make sure you're facing LEFT before the first ball hits the ground, and then keep running to the RIGHT. That should avoid all 3 balls (or 4 balls, in phase 3). As soon as the last ball goes over you, run back to the middle and repeat the process, but the ball will come from the other side, so mirror what you did before.
Scimitars: You have to find the safe spot where there's no scimitar above you. That's easy on phase 2, but very annoying on phase 3, since the gap moves around and you have to follow it closely. Get ready for some rage.
Pistols: On phase 2, just have Bubble Shield on and relax for a bit. On phase 3, go to the left corner of the screen when the shooting starts. As soon as the first pistols gets halfway through to you, move all the way to the right, and then all the way back to the left to avoid the pistols. Some people recommend crawling back to the left when you reach the far-right, but I never needed that. Instead, it helped me to jump at the end, in order to land close to the edge of the screen.
Bone platforms: This is when you can actually hit the boss. Careful not to get hurt by his shadows on the way up (they can also shoot, but you should always have Bubble Shield on). Usually, try to have Super Pike Balls take care of them, but don't take too much time, either. When you reach the top, make sure you have Super Milk and Super Pike active, and hit as fast as you can. Jump to make sure you hit on every chance you get. It's possible to defeat a phase in one go, but you'll probably need 2 rounds. Good news: the 2nd round will be exactly as the first one.

Phase 4 is A LOT easier. Phew. Make sure you have Bubble Shield on just to be safe, and activate Super Pike as well. Keep hitting him (won't deal damage, but will keep him in place) and use the SHOOT button when the crosshair is over his face. After about 1-2 sec, a cannonball will hit him. Do it 4 times and you're done!
Note that touching it won't hurt you, but he can still fire projectiles (that's why you should have Bubble Shield on).

Still need help? Check the video guide below to get an idea.
Video guide -- Note that this player (not me, by the way) is a bit stingy on items, but you should use them to be safe!

Special Weaponry
Defeat 250 enemies using Shantae's Monster Whipper!
Very hard to miss.

How: Just kill 250 enemies with your normal hair attack.


Risky's Business
Use a Pirate Flare to return to Risky's ship.


How: You need to use a Pirate Flare, which can be bough at the shop in Scuttle Town.


Tasty Treats
Sample the entire menu!


How: You'll have to use the following 6 items: Monster Milk, Super Monster Milk, Flesh Pop, Meat Chunklet, Bento Box, and Lobster Tail. Some people report that you have to quit the menu after eating EACH of these items for you to see the animation.


Ready for anything!
Defeat 50 enemies using Pirate Weapons.


How: You can unlock this as soon as you obtain the Pistol. Upgrading it helps.


Broken Bones
Destroy 20 bones with the Bubble Shield.


Where: Spiderweb Island, Cackle Tower
Requirements: At least 1 Bubble Shield, but more help. I got a few back at Saliva Island,
from Crabs and Mermaids.
How: With your Bubble Shield on, destroy bones thrown by skeletons at Cackle Tower.
The first screen where you can find them should be a good opportunity.


Nostalgia Trip
Discover the secret Labyrinth.


Requirements: Boots
Where: Saliva Island, Spittle Maze
How: On the first screen, use your boots to dash through the wall on the left. As soon as you get to the secret labyrinth, you'll unlock the achievement. You don't need to complete it, but you'll get some prizes for doing so.
Image with the exact spot:



Skilled Survivor
Complete the hidden training room.


Requirements: Cannon
Where: Scuttle Island, Royal Sewers, first screen to the right, with the blocks on the corners.
How: On the right side on the area, there are a few breakable blocks. Destroy the top ones (the Pistol helps) and leave the bottom one intact. After that, jump on that block and crawl to the right, where you'll fight some enemies to unlock this achievement.
Image with the exact spot:

These achievements are obtained by collecting Labyrinth Maps, Dark Magic and Heart Squids. Note that none of these achievements are missable, with one exception:

Squid Savior
Complete the game without any Health upgrades and all Heart Squids collected.


How: You have to find all of the Heart Squids, but you have to beat the game without ever melting any of them. It'll be a hard playthrough, since you'll never have more than 2 hearts for health.

Most of them are easy to find. Some Squids and Cacklebats require some backtracking after obtaining items, metroidvania style. You can also check if you're missing Squids/Bats from the Island selection screen. If you're having trouble finding them, refer to this map guide:
https://www.gamefaqs.com/3ds/689550-shantae-and-the-pirates-curse/faqs/73038

On the map!
Collect all Labyrinth maps.


Destroying the Dark Magic
Collect 50% of the Dark Magic.


Prepared for Battle
Collect all of the Dark Magic.


Gotta Get 'Em All
Collect 50% of the Heart Squids.


MELT! THEM!! DOWN!!!
Collect all Heart Squids.

There are two Speed Run achievements. Don't bother getting those before you've beaten the game at least once (SPOILER: and unlocked Pirate Mode, since you won't be able to do it otherwise).

These 2 achievements unlock AFTER the results screen, when you unlock the corresponding wallpaper, so don't close the game in frustration on the results screen if your achievement didn't unlock!

Speed Runner
Saved Scuttle Town as fast as possible!


How: Beat the game in less than 2 hours. You don't need to 100% the game, so just do it as quickly as you can.

Purple Haired Warrior Maiden
Defeat the Pirate Master's true form and save Scuttle Town in record time!


How: After a few tests, I first came to the conclusion that you need to complete the speedrun with 100% completion under 4 hours. My time was 3:28 (because I waited about 70 minutes to make sure I was over 3 hours to make my tests), but it's actually likely that you need to do it in 3:30. According to Jenna here in the comments, they beat the game with 100% in 3:37 and the achievement didn't pop, so the time is higher than 3:28 and lower than 3:37, so 3:30 makes the most sense. According to Cubey, though, they got the achievement in 3:31:18. Maybe the time is really 4 hours and Jenna missed something for 100%? I can't be sure.
By 100%, the game means getting all 32 Squids, all 20 Dark Magic, upgrade all weapons and acquire all skills. Yes, you need all Squids, all weapon upgrades and all skills. You do NOT need to collect dungeon maps! The game does say just "Defeat the Pirate Master's true form", but you actually need to beat the game with 100%.

For tips on how to obtain those 2 achievements, refer to this other guide by RavenMac:
http://gtm.steamproxy.vip/sharedfiles/filedetails/?id=841810374

Another nice guide is this one:
https://psnprofiles.com/guide/4314-shantae-and-the-pirates-curse-any100-speedrun-walkthrough


Note that you could branch the second speedrun from the first speedrun at some point. If you manage to beat the game in less than 2 hours, the extra 2 hours (or 1.5 hour) should be plenty to backtrack for anything you might have missed.

They're all story-related and cannot be missed. I'm listing them just to mention all achievements. There might be spoilers for you below, so consult at your own risk.

Ret-2-go!
Defeated the Ammo Baron.


Smells like victory!
Release the Ham Stink.


Green Thumb
Defeated the Cyclops Plant.


Eww! Eew! Eew!
Obtain Squid Oil.


Arachnophobia
Defeated the Empress Spider.


Avoided a Curse…
Obtain all three Mummy Sketches.


The fun part!
Obtain the Golden Pickaxe.


Ten-tickles
Defeated the Squid Baron.


It belongs in a museum!
Obtain the Fossil.


Mutant Buffalo
Obtain Manly Musk.


Graet Jobb
Defeated Dagron.


I GAINED THE ADVANTAGE!
Collect the Enchanted Blade.


Comfort and Convenience
Obtain the Spirit from Abner.


It ain't not gonna miss.
Help Ammo Baron fire the Palace Disruptor Cannon.


Hunk of Junk
Defeated the Steel Maggot.


Vanished into the eternal abyss…
Defeated the Pirate Master.

This section contains a few links to more information, in case you need more in-depth help:


YouTube Video -- All bosses (no items, no damage, normal mode)
YouTube Video -- Final Boss (100%) -- No damage


GameFAQs -- Full game map with all collectibles[www.gamefaqs.com]


Steam Guide for Speed Runs
YouTube Video -- Speedrun (video from guy who made the guide above)
PSNProfiles -- Speedrun text guide[psnprofiles.com]

As I mentioned above, I'll still add some tips on how to beat bosses without taking damage. Apart from that, if you find any mistake, please, tell me so I can fix it. Feedback is appreciated =)

I hope this guide helped you!