Here is the full list of all 76 Insane Robots achievements.
Take part in online multiplayer
Complete the tutorial
First successful attack
Win your first battle
Play 10 multiplayer battles
Reached rank 10
Reached rank 20
Reached rank 30
Reached rank 40
Reached rank 50
Completed tournament 1
Completed tournament 2
Completed tournament 3
Completed tournament 4
Completed tournament 5
Completed tournament 6
Completed tournament 7
Completed tournament 8
Gained 5 stars
Gained 10 stars
Gained 24 stars
Picked up 20 treasure
Picked up 50 treasure
Picked up 100 treasure
Purchased 10 augments
Purchased 25 augments
Purchased 50 augments
Won 10 battles
Won 25 battles
Won 50 batles
Won 100 battles
Won 200 battles
Gained 5000 cash
Gained 15000 cash
Gained 30000 cash
Completed 50 Swaps
Completed 50 Hacks
Completed 50 Glitches
Completed 50 Locks
Completed 50 combos
Won tournament with 1 life left
Refilled health from 1 to max in shop
Left acid cloud with 1 life
Unlock all robots (excluding DLC)
Upgrade a robot's health capacity to maximum for tournament
Upgrade a robot's augment slots to maximum for tournament
Attack with Harmony
Defend with Harmony
Use a teleport
Use a jet pack
Use a lucky augment in a tournament
Use a camouflage augment to hide
Use a strength increase augment in a tournament
Use a gas mask
Use a lightning conductor
Kill an enemy with a Deflector boost
Damage your attacker with a Deflector boost
Kill an enemy with a Booby Trap boost
Use a Diversion boost
Kill an enemy with a Rewire boost
Use an Inverter boost
Attack with 10 attack and 5 boost
Kill an enemy with a Damage token
Earn 1000 cash with a single cash token
Collect a treasure in the ring of death
Complete an arena without killing any robot
Kill two robots with one whirlwind
Elude a guard by using cloaking
Buy all augments from one shop
Win a battle in three turns
Perform an attack of value 25
Use balloon augment and land on a treasure
Finish a battle only using upgrade tokens with five fuel
Kill your arch-enemy twice in same tournament
Perform an attack in harmony after using a Rewire boost
Complete all nine quick battles