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