Here is the full list of all 14 Dig Dog achievements.
Reach the Desert
Reach the Hills
Reach the Mountains
Complete a loop
Complete a loop without warping
Complete a full loop in 3 minutes
Complete two loops
Collect 1000 bones
Die 1000 times
Kill 1000 enemies
Collect 1000 coins
Purchase an upgrade
Unlock all warp bones
Assist an enemy in killing another enemy