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.