Immediately after a challenge begins, go to the menu and switch to a faster vehicle or one that is more suited for the terrain. You can only do this once; the chosen vehicle will be the one you use for the rest of the game.
To get the "Sand to Stone" trophy, in free ride, go from White Flats Camp to Pinwheels Ridge Camp without resorting to the chopper. To get the "Salt over Snow" trophy, in free ride, go from Tsunami Reef Camp to Redrock Bluffs Camp without resorting to the chopper. You must not teleport directly from one camp to another. However, you can teleport to a previous Vista Point/Livery and still get the trophy.
Go to the northeast corner of the map. Note: You might have to look for some of the fuel. After knocking over all of the barrels, continue northeast until you respawn. More fuel will be there in the same location.