While the other guide is good, i have another option for you.
I honestly boosted this with my roommates account on another xbox.
If you have access to another xbox, account and copy of the game (if not bought digitally), this, along with the other online achievements, will be very easy.
If you have the game digitally, use the other account on your home xbox so they have access to it.
If you're lucky enough to have a trusted friend, or find an LFG post, then that will also help.
In the Multiplayer Tab, select Social Play and create a session. Go into the Lobby Settings.
Lobby Options:
Max Players - 2
Assists Restrictions are for the othercplayer, not you. I normally do:
Steering Assist - Off
Braking Assist - Off
Gearbox - Auto
ERS & DRS - Off
Assists: these are your own personal driving assists, so set them to your liking.
Track Select:
Set your season to 25 races (easier to keep track since you need 50 and 100 completed races), by just tapping
. If you want to skip a track, while it is highlighted, tap
to have the next track in that spot.
You can even do the same track over and over again if you like!
Weekend Structure:
Practice - Off
Quali. - Off (or whatever you like)
Session Length - Very Short (3 Laps) (or whatever you like)
I generally leave the weather and time alone.
Rules and Flags:
Rules and Flags - Off (this enables short cuts and corner cutting, even jumping the start without penalities).
Simulation Settings:
AI - 0 (again, your choice - there will only be the other player and you on track if done this way anyway).
Surface Type - Simplified (easier to run over if short cutting)
Car Damage - Off
(this is online so flashbacks wont be available)
Add/Remove AI:
I leave this at 0/19, and just press
twice to head back to the lobby.
Invite your friend/boosting account by pressing
. Once they are on the list, Ready Up and begin.
If using another account, simply pause them when qualifying starts (if you have it) and continue your qualification.
At the race grid, start the race with
and pause them. Once lights out (and awaaay we goo! -sorry, real F1 reference), the AI will take over and continue driving, so you can just drive on your account.
Finish 10 races (you do not have to win) and the achievement is yours!
This method is also good for the other online achievements of completing x number of races.
Note - Clean Races only count if you are driving, not the AI. You can cut corners and take shortcuts if rules and flags are off, you just cant bump into anything or anyone.