Here is the full list of all 16 Rarity Chase achievements.
Visit the main menu
All achievements completed
Become a winner on the 'Africa' map
Become a winner on the 'Ankh' map
Become a winner on the 'Icy' map
Become a winner on the 'Heart of Ice' map
Become a winner on the 'Islands' map
Become a winner on the 'Tiny Island' map
Use helicopter three times
Choose Anna as your character
Choose Joe as your character
Choose Dan as your character
Choose Alex as your character
Win three times
Use 10 ship tickets
Use 10 avia tickets