To unlock the Rootinest, Tootinest, Shootinest trophy in Borderlands: Game of the Year Edition, you will need to kill five Rakk (flying enemies) in under 10 seconds.
You can get this very early in the game. You will be directed to Skag Gully for one of the early missions, in the area, shoot some bullets to attract the Rakk, and then when they bunch together and swoop down to attack you, unload a fully automatic weapon into them.
You can see a video showing the location and method below (credit to Apache on YouTube):