Here is the full list of all 36 Lost and Hound achievements.
Chased the critters out of the camping area.
You opened the game! Woo!
Use Gus 5 times
Use Biner 5 times
Use Luna 5 times
Use Tigga 5 times
Upgraded Tigga completely
Upgraded Luna completely
Upgraded Biner completely
Upgraded Gus completely
Slide on the ice in the Alps
Found a gold nugget
Barked with Tigga in the Night Forest
Found which dog excels in sheep herding
Found which dog excels in truffle hunting
Found which dog excels in retrieving
Found which dog excels in gold
Discovered how to disrupt the airport scanners
Finish Venice without falling into the water accidentally
Discover the problems in the hospital