Here is the full list of all 40 Bish Bash Bots achievements.
Bash 500 bots
Bash 2000 bots
Bash 4000 bots
Build 50 turrets
Build 250 turrets
Build 500 turrets
Collect 5000 scrap
Push 100 bots into the pits
Scrap a turret
Equip a hat
Change your gadget
Drop an upgrade pack down into the pits
Drop a turret on a player
Destroy a Cannon Bot
Level 5 turrets to max in a game
Float straight into a pit at the start of a level
Finish a level with no turrets left
Complete a level with 1HP left on the EMP shield
Scrap a max level turret
Bluescreen at least 47 bots in a single level with the EMP
Don't let the EMP take damage in every level
Complete every challenge
Build one of each turret in a single level
Earn 80 scrap with the Scrap Investor gadget in a single use
Hit 10 bots with the Slam Hammer gadget in a single use
Collect 20 scrap with the Scrap Magnet gadget in a single use
Use the Teleport Pad gadget 10 times in a single level
Destroy 3 bots with the Airstrike gadget in a single use
Finish a level with 4 undetonated gadget Mines