This one is tedious but not difficult to do. You'll need the Gravity Boots to get all of the crystals so I suggest you wait until you have them. Also, the Map-O-Matic is very helpful in finding the crystals. Just be diligent and make your way systematically through the tunnels.
As far as killing the Amoeboids goes, the Rift Ripper, Qwack-O-Ray and the Plasma Coil are all very useful in ridding of them quickly. This could take you upwards of an hour but when you get all the crystals, take them to the Plumber to watch a cutscene and get your trophy.
This is also 1 of the 30 skill points needed for