Here is the full list of all 20 ArcRacer achievements.
Crash your ship
Earn your first gold medal in a non-tutorial event
Did you take notes?
Place in every Cyan League event
Place in every Cobalt League event
Place in every Amber League event
Place in every Beryl League event
Place in every Emerald League event
Place in every Fuchsia League event
Place in every Obsidian League event
Race with each ship at least once
Unlock every course in free race mode
Earn gold in every non-Master League
Earn gold in the Master League
Unlock the secret ship
Reach S+2 class in Zen mode
Pick a more retro visual style
Win a gold medal in the first lap of a speed lap event
Peruse the in-game guide
Reach full charge level six times in a single race