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 74 wins in a row against one player should net you this achievement (or 37 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.

Getting to rank one is actually fairly easy if you are even remotely good at the game. I suggest you complete the story mode first so you are familiar with the controls. If you have done this you should be better than most people online who have simply bought the cars through the DLC and are lacking in experience.

If you are any good at survival, this is the fastest way to progress. Most people find it really difficult and stressful but if you can keep a cool head, even when in last place you should be able to build your combo and rocket into the lead. The combo is vital in survival. Someone can overtake twice as many trucks as you but die every other time. If you are steady and avoid any dangers you will end the race with twice as much points as him.

You can race up to seven other people online, making a maximum of eight people in one race including yourself. You level increase at the end of each race is determined by the amount of people you bet, take away the amount of people who bet you. If you come 1st in a race with seven people. You will gain 6 ranks. If you come 2nd in a race with four people, you will gain 1 rank. If you come 7th in a race with eight people, you will loose 5 ranks.

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 25 shouldn't take more than about 18 to 22 wins. Depending on the amount of people in the race.