This video covers the fifth and final level ("Act 5: The Boss") in the METAL GEAR SOLID® Premium Level Kit for LittleBIGPlanet. Since it is not too difficult, I get all three Medals in one go. Though I also really liked the "The Collector" boss from Story Mode, the boss battle in this level is my favorite out of all of the "official" Media Molecule (Story Mode and DLC) LittleBIGPlanet 1 boss battles.
This recording will directly show you how to get the Speedy Rexecutioner Silver Trophy. (Note that the Trophy notification does NOT pop up because I already had that Trophy.) I claim that the first phase of the boss is the most difficult and that this is the phase that will probably trip you up the most. (I highly recommend taking out the first weakpoint in one firing cycle. It's tough to do with just one person as your aim needs to be more or less dead on as soon as the weakpoint is exposed, but it's certainly useful and possible to do so.) The second phase is the easiest, and the third isn't too bad either. Normally, the fourth and final phase can be a little tough (and time-consuming), but there is a nifty trick you can use to allow you to take down the final weakpoint effectively AND quickly.
Though this is last level of this Premium Level Kit, I still need to revisit Acts 1 and 4 to collect the remaining Goodies for 100% completion and the METAL GEAR SOLID® Booty Master Bronze Trophy.