First, the UAZ-469, the SUV the game starts you with, is a piece of junk. Handling in it barely improves with the upgrades and the suspension makes it bounce like mad, so what you want to do is avoid all upgrades and race it until you earn 1k coins, then go unlock the little black sedan (VAZ 2109).

The VAZ doesn't really need upgrading, it can handle everything in its starter configuration except steep hills, so make use of the wonky physics and cartwheel it through those spots. Spend the earned coins upgrading the UAZ instead, and finish all 12 races with it.

If the AI cars are being pesky and constantly trying to spin you out, brake and do a PIT spin on them. They take ages to recover from this and you won't see them again until near race end. There is no rubberbanding in the AI, but they will slow down and let you catch up to them sometimes if only to let them wreck you again. Knocking them into potholes is also a good ploy, unless you knock yourself in too, as there's no reset button.

To unlock the 24 races completed achievement, you must run the 12 courses with both the VAZ and UAZ, and must earn three stars (come in first) on every one of them.

To unlock the all upgrades earned achievement, 100% first one vehicle and then the other, backing out into the main menu after the last one should see the achievement unlock. Note races can be completed multiple times to earn enough coins to get all the upgrades.