DiRT

The online achievements for this game do not have to be done in ranked games despite what it says in the description.

I got all three in private player match races. However, it seems that now you need to have at least two players in the match for the achieve to pop.

This achievement due an update can no longer be done solo you will have to find a friend or booster to help you with this simply invite them to join you and finish with them staying at the start you win and they'll get a DNF is simplest. Note the online for this game is all but dead. (Repeat for live rally achievement)

Again I am willing to boost with people to get BOTH online achievements for them see other online achievement solution that i have posted for more details.

EDIT:
Again you must have another gold xbox live account, either another xbox you own or a friend. One of you search for a hill climb race and invite the other person, once in lobby vote for a hill climb big rig race as it won't automatically put you in one ( I know it's stupid) once selected, who ever needs the achievement just needs to win the race.

First off, I really suck at driving games, but even so, there are still players out there that occasionally have worse days than me. Finding them is how I got this. If you don't have a buddy to boost this with, keep signing out of sessions with good players and you will eventually find someone who are new to the game. Find a type of car and a track you feel comfortable with (e.g. Celica in Windy Peak Short), and keep voting for an option with one or preferably both of these.This will, of course, help you get an edge over the players even newer to this than yourself.

I started playing online today after getting the 1000 miles in career mode achievement, and the first races were on tracks I haven't driven on in a long time. After I logged out of this session (with one guy that constantly beat me with 20 + seconds), I found myself alone in a session, voted for a track and a car I felt OK with, and suddenly there were two other guys in the session. They were probably new, as they didn't even vote, and I soon got both this and the hill climb win achievement. As Earlydaze says in his solution, the online for this game is nearly dead, so there are not many sessions to choose from.