Birthday Gifts
A PlayStation Network connection is required for this cheat. Create a PSN account and sign in to the network. While setting up the account, claim that your birthday is the same as the current date. Start the game with that account and enter the GT Mode. The game will gift you a car or a coupon for a car. The year of the birth date determines which year the car comes from. Next, gift the free car to your main account to add it to the collection. This can be repeated endlessly for as many cars as wanted.
Rollover
The Rollover trophy, which requires that you "Flip a car over and total it," can be difficult to get under normal circumstances. The easiest way to win this trophy is by going through the last Chicane on Trial Mountain in a McLaren F1 at the highest speed possible. Hit as many of the curbs as possible. Do this twice in the same race to total the car as required.
Horsepower
Change the oil of a car immediately after winning or purchasing it. This immediately offers a small but noticeable boost to horsepower and speed.
Formula GT Car
The in-game Used Car Dealership (UCD) offers the special Formula GT Car on a random basis. The cars for sale refresh with six new models every in-game day. Completing a race or finishing a license test causes the game to progress to the next day. Days can be quickened by loading a license test and then skipping to the next test without actually racing it -- just make sure the loading screen shows up between the tests. An in-game day will pass, making new cars appear at the UCD. The cars cycle on a five-day basis, meaning at some point that the Formula GT car will reappear in the dealership.
Hidden Trophies
Some trophies are not listed but can still be won. The Endurance trophy requires completion of the Endurance series of race events. The Red Bull X1 Challenge trophy is rewarded by completion of the titular event. The Watch Falling Objects trophy is granted by intentionally making parts of the car fall off while driving, which is easiest to do with rally car doors. The Honda trophy requires taking a picture of a Honda, done easiest outside of the Honda head office in Tokyo on the R246 track, located on the left-hand side at the end of the pit exit. The Picture Exclusive trophy is granted by photographing someone special as he stands in Kyoto's Gio district -- zoom in on the man standing on the left of the bridge and use the auto-focus to capture a picture as he turns to look in your direction. The Portraitist trophy is granted by taking a photo of a solitary lady at the second photo location where a lady is sitting on a bench with a cell phone -- zoom in and use auto-focus and take the picture when the shot is clear.