Here is the full list of all 22 Grapple Dog achievements.
Collect all Gold Time Trial Medals
Achieve 100% Completion
Complete World 6
Collect all Purple Gems
Complete World 5
Collect 75% of all Purple Gems
Complete World 4
Collect 22 Gold Time Trial Medals
Complete World 3
Collect 50% of all Purple Gems
Complete World 2
Collect 25% of all Purple Gems
Collect 11 Gold Time Trial Medals
Knock down a Coconut with your Grapple
Let Pablo have a nap for a bit
Get a score of 10000 in Boomerang Bandit
Complete World 1
Complete a Bonus Stage
Complete a Time Trial
Pet the Dog
Complete a Stage
Give a Goat a Carrot