Here is the full list of all 31 Turbo Shot achievements.
Destroy an enemy in story mode.
Destroy 100 enemies in story mode.
Destroy 1000 enemies in story mode.
Complete the tutorial level.
Collect a datapad.
Collect 10 datapads.
Upgrade a powerup.
Upgrade 10 powerups.
Upgrade a powerup to max level.
Unlock a new character skin.
Unlock a new gun.
Win a PvP match.
Win 10 PvP matches.
Win 100 PvP matches
Win 1000 PvP matches
Reach the Iron League in PvP.
Reach the Bronze League in PvP.
Reach the Copper League in PvP.
Reach the Silver League in PvP.
Reach the Gold League in PvP.
Reach the Platinum League in PvP.
Reach the Painite League in PvP.
Reach the Stinchite League in PvP.
Complete an event.
Complete 10 events.
Open a Turbo Chest.
Open 10 Turbo Chests.
Claim the final reward tier of a Turbo Pass.
Reach the end of Chapter 1.
Reach the end of Chapter 2.
Toss 10 Blerphs to their doom. How could you?!