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