While roaming around the overworld, you will sometimes see chocobos walking around. If you mount on one of your chocobos (by pressing X + square) then you will be able to move fast enough to catch up to the wild chocobos (you can lock onto the wild chocobos with R1 to make this easier). Once you have caught up with them, press the square button to capture the wild chocobo.
Doing this once will earn you "Rookie Wrangler", and doing it 30 times will earn you this trophy. You can easily farm this in the Togoreth area of the overworld, since 4 or 5 chocobos spawn in that area. After you have captured them, leave and come back, and the chocobos will have re-spawned. See the following video guide: