Brotato

Mage is unlocked by default. To unlock this achievement, you need to beat the wave 20 boss using the mage.

EDIT: I should mention the sliders in the accessibility options that allow you to make the enemies easier to kill. Reportedly using these does not affect achievements, so if you're really having problems, try that.

Most of your damage will come from elemental damage. Melee, ranged, and engineering mods do nothing. That means that you can’t improve them; it also means that you can’t harm them, so any time the supposed downside to an item is one of those three things, then there really isn’t a downside.

I went with a lightning shiv approach. Try to get five of them, and keep upgrading them. The last slot I filled with a distance weapon that inflicted fire (wand, torch). Replace that with a flamethrower if you get the opportunity. Always upgrade your elemental damage if given the opportunity; always take a scared sausage to spread fire more reliably, or a snake to extend the fire’s spread. Build life steal up to 10-15% at most - it’s great, but it caps at 10 triggers per second, and if you get the flamethrower you’ll cap out. Speed is handy for the boss, although you can live without it. HP regen is good after you’ve gotten life steal up. Armor is good if cheap, but I rarely get it higher than 8 or so. Dodge is better, especially if you can get Adrenaline. Take those monkeys, too.

Your biggest problem will be the boss itself, especially if it’s the one with the random floor hotspots. There aren’t a ton of mobs for easy life steal, and if your speed is bad then you’ll need to position yourself in between the boss shots or risk overwhelming your healing speed. If you can do that at least half the time, and survive until he’s lost half his health, he switches to the circle pattern that surrounds you. You should be able to basically sit there and occasionally move out of the way of an enemy or two while time runs out or the boss dies, whichever happens first.