Credit for this method goes to Melia at ps3trophies.org. My estimate is that this technique requires 8-10 hours to get from level 1 to 40.
You'll need two controllers, some rubber bands and two PSN accounts (you can easily make a second account with a spare email address). This is a semi-automatic boosting method - it requires you to interact with the game every ~30 seconds but does not require you to complete the races yourself. You can easily multi-task with DVDs/TV etc.
Sign in to your primary account, start the game and enter a multiplayer lobby. With your second controller turned on, you should be able to sign in the second PSN account. Enter Custom Game and then Private Game and switch the game mode to Eliminator. Then go into game Mode Settings and change them to the following:
Perks: Off
Betting: On
Elmination Delay: 5s
Elimination Grace Period: 5s
Selecting the track and your vehicle is important; each succession of wins with each vehicle and on each map earns you bonus amounts of credits. For example, 10 races on a track earns 5,000 credits, 20 races earns 7,000 etc. The longer you stick with a vehicle or track, the larger the bonus, until you reach 50 races (earns 20,000). You may wish you switch every 50 races, or find it more efficient to switch more frequently (this will also help you earn the 'Decorated Stormer' trophy. You can check your progress for these Medals under My Motorstorm > Progress.
Once you have selected your vehicle and track, select Start Race. You will be taken to the betting sceen and at this time you must place a bet against your second account. You will only have a limited amount of time to confirm your bet and you must do this before every race.
You will need to use rubber bands to automate the winning process. I elected to use one rubber band for my primary controller (holding down R2) and two on the secondary controller (holding down R2 and the left thumbstick to the left). This ensured that both vehicles would move, but that the primary account would always win. If either vehicle fails to move for a short period, they are disqualified and your win streak is erased.
Once the race has finished and your primary account has won you will be taken to a screen which shows your winnings; you must press Square to bet your winnings for the following race. Each time you bet your winnings, the multiplier increases by x0.25 to a maximum of x5. Once you reach x5, you will effectively be earning 2,500 credits per race (as well as ~600 credits for the win). Therefore, it's best if you can commit at least 45 minutes - 1 hour for this method. With each win, the Bonus Pot will increase. Credits in the Bonus Pot will not be added to your level until you refrain from pressing Square at the end of the race. For safety, I tended to stop at 100,000 credits, as this game occasionally froze on loading screens.
Once you reach level 40, you may need to complete a couple more races for the trophy to unlock. You'll need 1,365,000 credits.
I feel this is a fairly comprehensive explanation of this method, but please let me know in the comments if there are any issues.