Here is the full list of all 100 Achievement Cage achievements.
Awake the fox
Pick up the apple
Give the apple to the fox
Receive roll ability
Hidden one :)
Touch Shift
Touch "3" key
Touch "4" key
Touch "1" key
Touch "2" key
Die in All Spikes
Die in All Saws
Touch and Pass All Tiles
Touch All 249 Tiles
Pass by All 665 Tiles
Die 100 times
Touch All Tiles
80 Achievements
90 Achievements
99 Achievements
Touch All Green Tiles
Touch All Yellow Tiles
69 Achievements
Click on the Sound Off button
Click on the Sound On button
Click on the Pause button
Die head down
Click on the hidden sus boy
Click on the Resume button
7 Corpses on Screen
Click on the Settings button
Click on the Menu button 1 time
Stay alive for 60 seconds
Touch Control
Pass by 600 Tiles
Die 50 times
Die in 20 Spikes
Rotate back up
Rotate back down
60 Achievements
Rotate head down
Click on the Youtube button
Rotate face down
Click on the Timer
Stand still for 15 seconds
Click on the Percentage
Click on the Screen?
Touch All Blue Tiles
Discover All Secret Rooms
50 Achievements
Die 30 times
Discover 10 Secret Rooms
Touch 200 Tiles
Jump in All Trampolines
Jump in 5 Trampoline
Die in 10 Spikes
5 Corpses on Screen
42 Achievements
Die Fast, like really fast
Pass by 420 Tiles
Touch All Red Tiles
Die 10 times
Die in the Moving Saw
3 Corpses on Screen
Die in 5 Spikes
Die 6 times
Discover 5 Secret Rooms
Pass by 251 Tiles
30 Achievements
Discover 1 Secret Rooms
Discover 3 Secret Rooms
Touch "Down" key
Jump in 3 Trampoline
Die 3 times
Play for 60 seconds
Touch 100 Tiles
Die in 1 Saws
Touch 75 Tiles
Stay alive for 30 seconds
20 Achievements
Play for 30 seconds
Touch "Space" key
Stay alive for 15 seconds
Pass by 100 Tiles
Touch "Up" key
Jump in 1 Trampoline
Touch 50 Tiles
Touch both "Left" and "Right" keys
10 Achievements
Play for 10 seconds
Touched 25 Tiles
Pass by 50 Tiles
Pass by 25 Tiles
Touch 10 Tiles
Touch "Left" key
1 Achievement
Die 1 times
Die in 1 Spikes
Pass by 10 Tiles
Touch "Right" key