Here is the full list of all 33 Icycle: On Thin Ice achievements.
Collect 100 ice cubes
Complete all 8 locations in the original Icycle 1
Complete all challenges for location 1
Complete all challenges for location 2
Complete all challenges for location 3
Complete all challenges for location 4
Complete all challenges for location 5
Complete all challenges for location 6
Complete all challenges for location 7
Complete all challenges for location 8
Complete all challenges for location 9
Complete all challenges for location 10
Complete all challenges for location 11
Complete all challenges for location 12
Complete all challenges for location 13
Complete all challenges for location 14
Complete all challenges for location 15
Complete all challenges for location 16
Complete all challenges for location 17
Complete all challenges for location 18
Complete all challenges for location 19
Complete all challenges for location 20
Discover secret area 1
Discover secret area 2
Discover secret area 3
Discover secret area 4
Discover secret area 5
Complete the main story
Endure 100 deaths
Collect 1000 ice cubes
Explode 100 bombs or sweets
Complete the final chapter Fin
Get 100% in all dreams from the scrapbook