Here is the full list of all 24 Chip's Challenge 1 achievements.
Completed all the levels
Completed all the levels between 141 & 149
Completed Force Field
Completed 20 levels still carrying keys
Completed all the levels between 121 & 140
Completed Icedeath
Completed Blobdance
Completed Totally Unfair
Completed a level with only 0.5 seconds to go
Completed all the levels between 101 & 120
Completed all the levels between 81 & 100
Completed Jumping Swarm
Completed 20 levels still wearing boots
Completed Cityblock
Completed all the levels between 61 & 80
Completed Rink
Completed all the levels between 41 & 60
Completed The Last Laugh
Completed all the levels between 21 & 40
Completed On The Rocks
Completed 20 levels on first try
Completed Blobnet
Completed all the levels between 1 & 20
Completed all the levels between 1 & 5