Grand Touring
-Complete each track in arcade mode at least once.

Versatile
-Win a race with each car on quick race mode.

Unrivaled
-Defeat every rival character in Arcade Mode at least once.
(You'll just get this one eventually by playing arcade mode a whole bunch. Rivals aren't that hard to beat.)

Diamond Cup
-Win Diamond Cup.
(Unlocked by winning all 3 other cups)

Invincible
-Win all races in a single cup.

No Road Not Taken
-Complete all possible routes in arcade mode.
Here's a very handy guide made by RacerBest that shows all 16 routes:
https://gtm.steamproxy.vip/sharedfiles/filedetails/?id=1393416297 (Doing any routes in reverse mode isn't required.)

Perfectionist I
-Get to every exit in arcade mode while beating all rivals on the way.

Perfectionist II
-Win all races on every cup.

Perfectionist III
-Get all achievements.
("Deja Vu" and "Transluscent Black Capes" aren't needed.)

Supersonic
-Stay on the Slipstream for more than 15 seconds on any mode.
(I think it's easier on arcade mode, but don't quote me on that.)

Intangible
-Complete an Arcade Mode run without touching anything.
(Anything aka both cars and scenery. Apparently, you will unlock this achievement anyway as long as you perfected at least 1 stage.)

Minimalist
-Win a race in Grand Prix mode without any car upgrades.
(very easy on first race of any cup on normal.)

Transluscent Black Cape
-Defeat Camilla (Purple haired girl) in Highgate Cemetary.

Deja Vu
Defeat Tofu Boy in Akagiyama.

Thanks to everyone who helped make this guide!