Here is the full list of all 15 A Story About My Uncle achievements. It takes around 12-15 hours to unlock all of the achievements on Windows.
Earn Gold medals on all Time Trial levels
Complete Ice Cave using less than 115 Grapples
Complete Ice Cave without failing
Find all 25 Collectables in the game
The floor is lava.. or well, ice.
Interact with all the optional story objects
Complete Star Haven using less than 55 Grapples
Complete Star Haven without failing
Complete Maddie's little game
Complete Chasms using less than 34 Grapples
Complete Chasms without failing
Complete Village using less than 20 Grapples
Complete Village without failing
Complete Sanctuary using less than 23 Grapples
Complete Sanctuary without failing