Here is the full list of all 22 get REKTorized achievements.
Earn every achievement
Unlock every Mетелик пір'я ship
Loose a RoboDrone lasering you
Win your first race
Win your first online race
Kill all 6 AI ships in a race
Collect every insignia
Travel across the secret path at Tropical East. Jet
Finish the story
Take a photo
Finish a race with 0% energy
Collect 7 POI's in HauntedCity
Get killed by a Zombie in HauntedCity
Fly a local TimeKiller record on every track using every speed class
Kill your first enemy
Fly on Ribon
Complete the first story event
Obtain every weapon in a SingleRace
Fly into your own Flash_Bomb
Find the dragon cave in Drachenlair
Obtain gold in all story events
Complete the Tutorial