Here is the full list of all 23 Rocket Rumble achievements.
Play a match in Asteroid Field
Play a match in Caustic Canyon
Play a match in The Pirate Bay
Play 10 Quickplay matches
Play 100 Quickplay matches
Play 500 Quickplay matches
Win 1 Race
Win 10 Races
Win 50 Races
Win 100 Races
Die 25 Times
Die 100 Times
Die 500 Times
Die 1000 Times
Win 10 Quickplay games as Pepper
Win 10 Quickplay games as Ophelia
Win 10 Quickplay matches as Riku
Win 10 Quickplay matches as Bert
Customize all your characters
Play a match in Holo Night
Win 10 Quickplay matches as Lori
Win 10 Quickplay matches as Ghost
Play a Quickplay Game during an Event