Here is the full list of all 40 Innoquous 5 achievements.
Complete 5 levels in Bunny Hunt mode.
Collect 14 notes.
Complete 25 levels in Standard mode.
Collect 5 notes.
Collect 3 notes.
Complete 5 levels in Standard mode.
Complete 50 levels in Standard mode.
Complete 100 levels in Standard mode.
Complete 175 levels in Standard mode.
Complete 5 levels in Conditional mode.
Complete 25 levels in Conditional mode.
Complete 50 levels in Conditional mode.
Complete 100 levels in Conditional mode.
Complete 175 levels in Conditional mode.
Complete 5 levels in Fiery Floors mode.
Complete 25 levels in Fiery Floors mode.
Complete 50 levels in Fiery Floors mode.
Complete 100 levels in Fiery Floors mode.
Complete 175 levels in Fiery Floors mode.
Complete 25 levels in Bunny Hunt mode.
Complete 50 levels in Bunny Hunt mode.
Complete 100 levels in Bunny Hunt mode.
Complete 175 levels in Bunny Hunt mode.
Complete 5 levels in Time Attack mode with at least a bronze medal.
Complete 25 levels in Time Attack mode with at least a bronze medal.
Complete 50 levels in Time Attack mode with at least a bronze medal.
Complete 100 levels in Time Attack mode with at least a bronze medal.
Complete 175 levels in Time Attack mode with at least a bronze medal.
Complete 5 levels in Chaser mode.
Complete 25 levels in Chaser mode.
Complete 50 levels in Chaser mode.
Complete 100 levels in Chaser mode.
Complete 175 levels in Chaser mode.
Collect 50 notes.
Collect 100 notes.
Die 1,000 times.
Toggle switches 1,000 times.
Fall through 1,000 breakable floors.
Have guns break 1,000 floors.
Tag 1,000 guns.