Here is the full list of all 28 Ducky's Delivery Service achievements.
Deliver flyers to an area.
Clear the special delivery stage in Oak Town.
Clear the special delivery stage in Chia Shores.
Clear the special delivery stage in Pepper Cave.
Clear the game.
Earn three stars in an area.
Earn three stars in all areas.
Earn four stars in an area.
Earn four stars in all areas.
Earn three stars in an area without damaging a single package.
Earn a time attack A rank in one area.
Earn a time attack A rank in all areas.
Earn a time attack S rank in one area.
Earn a time attack S rank in all areas.
Throw a package into a mailbox from over 5 meters away.
Throw a package into a mailbox from over 10 meters away.
Fly from one end of Chia Shores' Beachfront area to the other, without landing or touching anything.
Fly from one end of Pepper Cave's Ghost Tunnel area to the other, without landing or touching anything.
Fly under the windmill in Oak Town's Town Square area from right to left, without landing or touching anything.
Clear the special delivery marathon.
Earn an A rank in the special delivery marathon.
Earn an S rank in the special delivery marathon.
Earn an A rank in the flyer marathon.
Earn an S rank in the flyer marathon.
Earn an A rank in the score marathon.
Earn an S rank in the score marathon.
Score 20 or more points in Ghost Survival.
Earn all other achievements.