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