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