Here is the full list of all 8 Garden Buddies achievements.
Finish tutorial.
Move your body and unlock Bulby in story mode.
Catch them all and unlock Betty in story mode.
Clean Bolita and unlock her in story mode.
Rock the guitar and unlock Aspen in Story mode.
Pet the frog in story mode.
Make a tower of stones and unlock stone buddie in story mode.
Finish story mode.