Here is the full list of all 87 Trimps achievements.
Reach Z30 with no respec and 60 or less He spent
Complete Spire II on the Coordinate challenge
Gain at least 01189998819991197253 He from one Bone Portal
Get 10 Red Crits in a row
Defeat an enemy on Obliterated
Earn a Challenge2 bonus of 2000%
Complete a Bionic Wonderland map 45 levels higher than your Zone number
Complete Lead with 100 or fewer lost battles
Complete Lead with 1 or fewer Gigastations
Complete Watch without entering maps or buying Nurseries
Beat Toxicity, never having more than 400 stacks
Find an Amalgamator on Z1
Defeat a Healthy enemy with 200 stacks of wind
Bring a world enemy's attack below 1
Build up a Poison debuff that's 1000x higher than your attack
Reach Z60 with 1000 or fewer dead Trimps
Complete The Spire with 0 deaths
Kill 1M enemies in your Spire
Equip a Magmatic Staff and Shield
Use up all 7 Daily Challenges
Overkill an Omnipotrimp
Beat Crushed without being crit past Z5
Overkill every possible world cell before Z60
Complete a Void Map at Z215 on Domination
Spend over 250K total He on Wormholes
Beat Balance, never having more than 100 stacks
Spend at least 10 minutes breeding an army with Geneticists
Break the Planet with 5 or fewer lost battles
Reach Z60 with rank III or lower equipment
Reach Z75 without buying any housing
Reach Z60 without hiring a single Trimp
Equip a magnificent or better Staff and Shield
Own 100 of all housing buildings
Find an uncommon heirloom at Z146 or higher
Kill an enemy with 100 stacks of Nom
Beat a Lv 60+ Destructive Void Map with no deaths
Reach Z120 without using manual research
Reach Zone 10 with 5 or fewer dead Trimps
Attack 20 times without dying in Electricity
Kill an Improbability in one hit
Reach exactly 1337 He/Hr
Have over 1M traps at once
Die 50 times to a single Voidsnimp
Complete the Dimension of Anger before buying Bounty
Create a perfect Map
Complete a Zone above 99 without falling below 150 stacks on Life
Build your 10th Spire Floor
Complete Corrupted without Geneticists
Beat the Spire with no respec and 100M or less He Spent
Beat Z75 on the Scientist V challenge
Kill an Enemy on Eradicated
Complete Spire V with no deaths
Build your 20th Spire Floor
Complete a Bionic Wonderland map 200 levels higher than your Zone number
Beat Spire II with no respec and 1B or less He spent
Beat Imploding Star on Obliterated
Close 750 Nurseries at the same time
Earn Dark Essence with no respec and 0 He spent
Reach Magma on Obliterated
Break the Planet on Eradicated
Reach exactly 1337 Rn/Hr
One-shot a Dimension of Rage enemy on Unlucky while Unlucky
Complete Downsize with an equal amount of Huts, Houses, Mansions, Hotels and Resorts
Complete Transmute without hiring a single Trimp
Complete Unbalance with 500 stacks of Unbalance
Complete Bublé without using Prismal or respeccing Perks
Complete Duel without ever falling below 20 points
Complete Melt without ever having more than 150 stacks
Complete Trappapalooza without Trapping on or above Z50
Complete Wither with 10K stacks of Hardened
Reach a session score of 100-0 at L5+ in SA
Kill a L20+ SA Enemy without Shock, Bleed or Poison
Complete Revenge with exactly 19 stacks
Complete 80/80 quests on Quest
Complete Archaeology without ever having more than 0 of one Relic
Complete Storm without ever encountering a Stormcloud
Complete Insanity with 500 stacks without running a map above lvl 50
Finish Berserk after reaching 20 Weakened Stacks before Z100
Reach 100 Swarm Stacks by Z120 then complete Exterminate
Reach L19 Cruffys by Z70 then complete Nurture
Collect 7500 Runetrinkets
Complete all 25 Mayhems
Complete a Z155 Void Map with 10 Gas Brews and 0 Void Pots
Complete Hypothermia with at least 400 Embers
Complete Glass without ever having more than 2 stacks
Beat a level 100 SA Enemy
Kill a Bad Guy with two different Mutations