Here is the full list of all 21 Loot Hound achievements.
Find 8 uncommon loot items
Own 3 dogs
Find 7 rare loot items
Own 2 dogs
Find 10 common loot items
Find 5 legendary loot items
Complete 1 loot set
Complete 3 loot sets
Complete 5 loot sets
Escape the park patrol
Find a new loot item in Scavenger Hunt mode
Find 7 loot items in rock
Find 7 loot items in enclosed spaces
Find 7 loot items guarded by animals
Solve the Buxton Wheat Field mystery
Maximise a skill for two different dogs
Discover every loot item