Here is the full list of all 31 Mail Mole achievements.
Save Carrotland's Summer Festival
Recover all the power cells of the second tower
Complete Magma Rocks
Find all the radishes
Complete Spooky Swamp
Recover all the power cells of the first tower
Complete Coconut Island
Beat Pukat's fourth machine
Complete Dry Canyon
Beat Pukat's third machine
Expand your world
Complete Yeti Ridge
Beat Pukat's second machine
Complete Ancient Temple
Save 1000 carrots
Win a race against Mecha Moles
Meet Scarlett the Skunk
Complete Carrot Fields
Save 500 carrots
Beat Pukat's first machine
Save 300 carrots
Reopen Rick's Store
Finish the tutorial
Get a gold medal
Purchase an outfit
Recover all power cells, win all races, get all medals, buy all the clothes
Purchase 20 outfits
Purchase all outfits
Win all the races against Mecha Moles
Get 15 gold medals
Get all gold medals