here's my TL;DR solution for this achievement.
requirements:achievement is weird and description is wrong. for progress to count, you must reach and start wave 21.
to play this mode, on any map press
then
to switch to endless
there are progress/level restrictions, so it may be greyed out.
endless mode is hard. do not bother trying to play until you beat all 13 maps on tier 1 and have access to olympus pillar and cannon sentry traps. you will not get far otherwise.
my recommended class: Mercenary
why: best class in the game IMHO. Maybe I was lucky with equipment, but my merc was the only class I could play as that could be surrounded by enemies getting punched by them all at once and take 0 damage. Sorceress is an ok alternate, but struggles on later waves. For marksman, are you kidding? He's really bad!
mandatory skills by tier and order of importance:tier 1:
Strike + both passives
Mark of the Keeper
Contraption Expertise
Touch of Death + Lingering Curse
Rage
Ghastly Shape (just 1 point. useful for getting around map faster)
tier 2:
Chain Snare + Barbed Hooks (stupidly useful crowd control. Electrified Chains passive does not appear to work)
Spring Mechanism Expertise
Talent For Invention
Mark of Craftsman
tier 3:
Bash + Murderous Blow (main source of damage vs armored/tanky enemies)
Iron Skin
Mark of the Slayer
Fury
Selective Monster Breeding
traps (categorized):most important:
essence trap: 3 stars in upgrade 1 and 15-20 points in both passives
traps used to deal pure damage. All have 3 stars and 20 in both passives:
Acid Geyser
Olympus Pillar
Cannon Sentry
Portal Glyph - the best thing about this trap is the description is wrong! A portal trap can teleport 1 enemy multiple times. One with upgrade 2 fully leveled up can and will keep chewing off 30% of an enemy's health until they die. Unfortunately this trap does not work on giant enemies.
traps used to slow enemies
icicle field: 3 stars in upgrade 1
frost pillar: 3 stars in upgrade 2 & 3. I upgraded Focus Crystal to 10
gun sentry: 3 stars in 2 & 3. Points in Improved Cartridge useful, but not necessary
monster cage: 3 stars in 1 and 3 at least. 20 both passives. this trap is used tie up and distract enemies letting turrets hammer enemies to death
other useful traps
stasis trap: no upgrades necessary.
I use this sometimes because it completely freezes most enemies in place for a few seconds.
archer post: 3 starred all upgrades
suicide swarm nest: 3 starred 1 & 2
Summon trap locations are not always ideal for monster cages. Sometimes the traps are too out of the way of creep paths, and its better to put the archers for ranged attack. Sometimes the summon traps are on top of enemy paths with no nearby turrets to do the killing, so I use suicide swarms instead.
strategery:here's a mostly effective strategy for reaching wave 21 on all maps in endless:
wave 1: put essence traps in ALL mechanical ground trap slots. For real. Endless is EXTREMELY stingy with essence. You get a bonus to essence traps the more essence traps there are, and the more essence you get faster, the better. I would upgrade the essence traps I found myself camping killing enemies on top of.
I would also upgrade the essence traps within kill boxes. A kill box would be any place enemies would cluster up around an essence trap and get pounded by turrets. A GREAT way to set up a kill box is if there's a mystic ground trap slot adjacent to the essence trap. I would slap a stasis trap down. It doesn't need to be upgraded and will freeze all enemies that aren't giant. They'll usually get blasted by turrets and give you an essence bonus. This also happens with summoning traps. You can usually tell if monster cage will distract enemies on top of an essence trap radius.
phase 1: you should easily get 1000's of essence within the first wave. What I'd do is build up around essence traps trying to make kill boxes upgrading the traps as much as possible. Then I'd gradually fill in the remaining empty trap slots.
at the end of phase 1, I'll have traps built on all the available slots, all of them fully upgraded. What you build is up to you. Typically I'd have raw damage traps in everything excepting near the base where I'd put stuff to slow small fast or large beefy enemies who get through.
With essence traps everywhere and both passives to 20, you ought to reach this point very quickly. Easily within the first 5 waves on most maps.
phase 2: this is where I sell the essence traps and replace them with acid geysers. none of the other ground traps are really worth it. as difficulty increases, the main purpose of the acid traps is to give enemies 90% debuff to physical damage.
for almost all of the maps, you should be able to get to wave 21 without much trouble. In many cases without any damage to your base.
EXCEPT!
For map 12 wounded crag. This is the only exception. Its actually kind of hard.
here's what will eventually happen. Waves will end with a tripod spawning at the lower left portal and a champion jellyfish enemy will spawn at the top left most portal. Everything will be dead except for these two enemies, they will be approaching from 2 different directions and will hit your base at the same exact time. As the difficulty ramps up, these two enemies will become such damage sponges, you will only be able to kill 1 of them and not have enough time to bash through the insane health of the other before it gets into your base and kills your d00dz. The best thing you can try to do is throw icicle fields down on the lower left to slow the tripod down and try to put turrets that slow the jellyfish, but I can tell you from experience @ wave 17-18 it becomes nearly impossible to kill both. I'd recommend focusing on the tripod since he can spawn spiders. I can't remember how much damage the jellyfish do to the base, but it is at least 2.
Have fun with this achievement. Its more time consuming than it is difficult.