Here is the full list of all 40 Inertial Drift achievements.
Complete the tutorial
Use the Drift Stick
Compete in a race
Compete in a duel
Compete in a ghost battle
Compete in an endurance event
Compete in a time trial
Compete in a style event
Set a leaderboard time in Arcade Time Attack
Set a leaderboard score in an Arcade Style event
Unlock the Boba
Unlock the Katana
Unlock the 7D
Unlock the Bullet
Unlock the Ventus
Unlock the Jet Z 880
Unlock the Raptor
Unlock the Gecko RX
Unlock the Jester
Unlock the Gladio
Unlock the Impuls
Unlock the Supreno
Complete Edward's story
Complete Ada's story
Complete Ibba's story
Complete Viv's story
Complete a story play through on "Xtra Crispy"
Complete 10 laps in practice mode in one session
Win a race
Win a duel
Beat the target time in a ghost battle
Earn gold in an endurance event
Earn gold in a time trial
Earn gold in a style event
Complete an event on every track
Complete an event on a reverse track layout
Hit a checkpoint with less than 1 second left
Earn a platinum medal
Achieve 100% on a story mode playthrough
Complete grand prix mode with every car