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