Here is the full list of all 17 Dead Climb achievements.
Grab the wall 10 times
Grab the wall 100 times
Grab the wall 1000 times
Fall during climbing
Fall 10 times during climbing
Complete the level as a man zombie
Complete the level as a woman zombie
Complete each level in each gameplay mode
Complete Small Island
Complete Dust Land
Complete Winter Land
Complete Raw Land
Complete Canary Island
Complete Tropical Island
Complete Arctic Land
Complete Chinese Mountains
Complete Desert