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