The Schell Games logo appears at the end of the credits. It takes 100 hits to destroy. Your own ship has three hit points.
The best way to get this is to spend the early part of the credits sequence pressed over towards the right of the screen, destroying the credits before they can center themselves. Once you get to the end of them, you'll want to move over to the right and immediately start spamming shots at the logo as fast as possible, moving over to stay underneath it until it centers itself. This should give you about 25 hits on the thing.
After this, your goal is to avoid the shots it drops while dealing damage. The best way to do this is to stick over towards the left-hand side of the screen; the first two back-and-forth sequences give you an opportunity to unload a lot of shots on it while it is slowing down to start its way back across the screen, while the next set of two will drop multiple bombs (i.e. two instead of one) in this region, making it nigh-impossible to dodge them both (or indeed, either of them) if you stay there.
The best way to win, then, is to weave in and out of that left-hand edge, dodging bombs and doing as much damage as possible for two sequences, then staying out of the corner for the next two sequences before going back into the corner.
If you do this, you should be able to kill it fairly rapidly, assuming you have a good trigger finger.
Very few people have managed to get this achievement as of the time of writing.