Split/Second

You can better your online form through private matches. If you invite one person to the game and beat them (with AI turned off) you will better your rank by 1. If you have 2 people (including you) you will better your rank by 2, 2nd place gets nothing (but doesn't down rank), and 3rd place loses 1 rank. So 24 wins in a row against one player should net you this achievement (or 12 wins against two players).

You could also work on this by playing public matches. You can better your rank faster by beating 7 players (you also get points for finishing in the top half of the pack). However your rank can drop easier playing public matches. You lose 10 rank for quitting early. Also note that people online use the best cars, so you are likely to lose often if you haven't unlocked all the cars.

Using the mode Elimination is the quickest way, since a race is approx 1 minute for 2 people and 1 minute 20 seconds for 3 people. With loading screens and other waiting an elimination round is approx 2 1/2 minutes.

Courtesy of BrutishMuffin :
you can lose up to 7 ranks in a race with 8 people. It goes by how many people you beat compared to how many people beat you.
2 People: +1, -1
3 People: +2, 0, -2
4 People: +3, +1, -1, -3
5 People: +4, +2, 0, -2, -4
6 People: +5, +3, +1, -1, -3, -5
7 People: +6, +4, +2, 0, -2, -4, -6
8 People: +7, +5, +3, +1, -1, -3, -5, -7

Courtesy of PackageDonkey:
You can backup your save via memory card/usb stick and restore it (restoring your level) if you have any issue with a few bad races in a row. This would also allow you to trade first place with someone else, and restore your first place position after you've given them their wins.

If you are doing it legitimately. In race mode.

The thing with the online racing is, when you keep winning you start further back on the grid.

If you are having trouble competing, People tend to ram you or get in the way at the start. Quit out of the lobby after about 4 or 5 wins and search for another game and you will start at the front of the grid again.

Even if you end up back in the same lobby you will start towards the front.

Getting to 75 shouldn't take more than about 6 or 7 wins. Depending on the amount of people in the race.

if you decide to boost the online achievements





It is impossible to boost without "sacrifying" the form level of a chosen player.

If you boost with 2 players, at each race, the winner gets +1, the loser gets -1.
So alternating winning will not work, and leave you at same level without progression.

One of you will have to finish at top level, the other one at the bottom.

Run 99 races with always the same winner,
(he will get Start, Good Form, Out of Reach, World Beater)
then run 99 races with the other player winning all,
(he will get Start, Giant Killer, Good Form, Out of Reach, World Beater)
the run a race with the first player as a winner again.
(he will get Giant Killer)
At the end player 1 will be of form 98, and player 2 of form 2.

For each half of the session,
only the player that needs to win requires to be at his controller.
The other one can go away from his xbox/tv.

The player to win starts a private elimination match with no AI, any track.
(elimination will only last ~1 minute)
He invites the other player. The other player accepts the invite.
From there for all the levelling of player 1, no interaction of player 2 is necessary.

Once player 1 at the top, swap and repeat.
Do not forget to swap again for one race at the end, for the last cheevo.