This guide will attempt to be as brief as possible. If you are new to the game I recommend looking at other guides or just learn by doing.

Heroes used:

LEVEL FIRST
Hermit - Builder
Initiate - Builder
Huntress - Builder
EV - Builder

LEVEL SECOND
Adept - Builder
Apprentice - DPS

MISC
Summoner - To pick up chests

Always run on hardcore.

The first goal will be to clear the first wave of "Challenge: Raining Goblins. This guide assumes starting from absolute zero, so we will need to unlock it first.

Path:
The Deeper Well - hard
The Deeper Well - insane
Foundries and Forges - insane
Magus Quarters - insane
Alchemical Labratory - insane
Challenge: Raining Goblins - nightmare (first wave)

I did these with just hermit. Perhaps there exists a more optimal hero composition. I failed a few times on magus quarters before I cleared it, but it got progressively easier as it gave the chance for more loot to drop that made my hermit stronger. If you are having issues, you might just want to drop the difficulty to hard (at the expense of worse loot). Once you have cleared the first four maps, raining goblins should be unlocked. The strategy to clear the first wave with hermit is to place seed bomb towers around the core, some facing outwards and some facing in. During the wave you can distract/stun the goblins by doing your spin move. Don't forget to loot the chests.

Tip: Pirate invasion chests drop gear right away, no need to deal with enemies. You can abuse this to perhaps get some starter pieces and mana. I didn't do this but you certainly could to make it a bit smoother.

Good job clearing the first wave of raining goblins. Now we are looking for some upgrades that will enable a massive leap in stats.

Path:
Challenge: Raining goblins - nightmare (as many waves as you can clear)
Bonus: The Tinkerer's Lab - nightmare (first wave)
----------------------------Level up first set of heroes to level 74--------------------------------------------
Embermount Volcano - nightmare (first wave)

We start of by running raining goblins until failure over and over and collecting the loot from chests. You will need to be lucky and find pieces with nice tower stats. Once your hermit has about 200 tower damage and other tower stats around 30-50, it should be possible to move on and clear the first wave of tinkerers lab. It might require some trial and error before you manage it. If you cannot, you can always stay longer at raining goblins in search for even better gear.

The strategy for clearing first wave of tinkerers lab as a hermit is to use a lot of seed bomb towers and possibly a few web walls at specific locations. After clearing the first wave as a hermit, you should get a lot of levels. Go and open the chests and stare at the mythical gear you cannot yet equip. If you are lucky you can find mythical cardboard tubes which you are able to equip despite not being level 74. After clearing the first wave once, you should be able to do it again but this time with four splits. Keep running the first wave and picking up gear from the chests until all of the four first heroes are level 74 so they can equip mythical gear. I recommend not having all four characters in at the time of opening the chests (press F7) because you want to be getting armor, not lots of bad weapons.

Now that all of your four first heroes are level 74, they can equip the mythicals you have found. By now they should have about 1000 in their main stat and 500 in their sides.

Next up is embermount volcano first wave. The first wave of embermout volcano only has goblins, archers, orcs and spiders. This means we can abuse gas traps hard to give our defences a lot of time to attack the enemies. You should watch out for spiders webbing your towers. The strategy is to have strength drain + ensnare auras at each crystal. Then two gas traps at each crystal. Use seed bomb towers close to the middle bridge between the crystals. One stack at either side of the bridge. Protect and buff them with a buffbeam and two reflects each. Round out the build with a hermit pylon on either side to buff the range of the traps and auras. Possibly add proximity mine traps under the seed bomb towers to help clearing the spiders. After clearing the wave, don't forget to loot the chests.

Good job clearing the first wave of embermount. Notice how much exp you got for it and that the chest loot is a little better than what it was on tinkerers lab. You should get comfortable with embermount volcano because you will be there a lot.

Path:
Embermount Volcano - nightmare (first wave)
Moonbase - hard
Embermount Volcano - nightmare (first wave) (Level other heroes here)

Now that you have cleared the first wave of Embermount, do it again. And again. And again....
You might want to make a summoner at this point and have it in for one of the runs to give it some levels and put them in speed so you can use it as an armor vacuum cleaner. Collect and distribute the best builder armor you can find for your heroes (don't forget about set bonus).

When you get tired of Embermount Volcano, you can go to moonbase. We are running Moonbase in the sole interest of getting the fish in a bowl pet. To get the pet you need to do the secret. If you don't know how to, look on youtube. I made a single core build, letting all but the south core be destroyed. The build consisted of gas traps, auras, seed bomb towers, a mushroom spore tower, a forest golem, a pylon and a buff beam. Make sure to have in all four splits for the last wave to get four fish in a bowl instead of just one. Run this a few times until you are satisfied with the fish you found. This should have given you a significant stat boost of around 500 in most of your tower stats.

Now it will be a little easier to run embermount. Run embermount and start to level an adept builder and an apprentice dps. Keep looking for better armor for all of your characters. Once all of your heroes are sufficiently leveled and have around 1500 - 2000 in their main stat and 1000 sides, you are ready to move on.

Great, now you actually have some characters that can do something. We are nearing the end of the guide. Now there is just some housekeeping to do before the grand finale.

Path:
[ Servants Quarters - Endless Spires ] - insane
Raining Goblins - nightmare

Since the goal of this guide was to be able to run Challenge: Assault, it needs to be unlocked first. Completing campaign maps from Servants Quarters through Endless spires on insane should be super easy by now. Just put down some aura stacks and maybe a pylon. Do whatever you want for these maps here honestly, you are way overpowered for these.

The next step is to run raining goblins on nightmare to completion. It should not be difficult for you. We are looking for the end of map reward, "Goblin Overlord's Charge". This weapon will be used on our dps apprentice to be able to clear the boss on the next map. Look for a decent one with 200+ upgrades. Use the upgrades to upgrade it in the following order of priority: additional projectiles, charge speed bonus, projectile speed bonus and Base Damage.

Now is a good time to look over your characters, see if you can improve anything about them. You should especially pay attention to your dps apprentice to make sure it has the survivability it needs. Possibly upgrade his resists.

Now for the final challenge.

Path:
Tropics of Etheria - hard

The reason we play Tropics of Etheria is to get the staff it rewards: Dragon Staff. The dragon staff is a weaker version of a moon staff. Moon staffs are one of the weapons typically used to run assault easily. We settle for the Dragon staff because it is much easier to obtain.

The build I used was to put one aura stack at each core along with a buffbeam, reflect and a golem. For the crystal at the coast, two lightning towers and two deadly strikers facing out. For the crystal on the hill, two deadly strikers facing outwards in different directions. The rest of the defence units were used on lightning towers at the core on the hill. For the first wave I built everything on the coastal core except for the golem and for the core on the hill, only one lightning tower and a fireball tower just to clear the first wave. Then on the second wave completing the build. During the waves, I ran around on the dps apprentice with the overcharge ability active to help clear ogres at the crystal on the hill (and also upgrading both buffbeams). For the last wave you can bring in 3 other apprentices/adepts to get more rewards. The boss fight has two bosses, one special kraken and one special demon lord. Use your Overcharge ability on the apprentice to deal more damage to the bosses. I suggest you stand near your towers on the hill so that the golem can heal you during the boss fight. Try to target the demon lord first and dodge the weird balls it shoots at you. Then take care of the kraken. You might need to lure it to your location. Just make sure not to get hit by it all too much and die.

Once you complete the map, you will be awarded with one dragon staff per split. Some of them might be quite bad. Look for the one with the most upgrades and best initial stats. You might need to run the map again if the stats you got were too bad.

Congratulations. Once you have upgraded your Dragon Staff (correctly), you will be able to run Challenge: Assault on Ruthless hardcore. Just give the Dragon Staff to your dps apprentice and you are ready. Look on youtube if you don't know where to shoot.

Farming the map will give you lots of rewards in the form of pets, weapons and armor. Furthermore, you can sell whatever you don't want for massive mana gains.

Thanks for reading!