I think most of them are for collecting all of a type of item. I only have one, for collecting every type of gem available while mining, but there are many more, one for collecting musicblox, etc. Someone more trophy-laden than I could give you a list. I bet Hburger could give you a link to a list, even. :D
Nanookie, which are the gems that you need? I currently have the ruby and diamond. What else do I need? Aren't those just two ways to ask the same question? Why am I asking so many questions? I guess I should go now?
Is the trophy for all musicblocks, or just each set of colors (e.g. DR-1 through DR-5)? Don't the musicblocks disappear when you collect them all? Does the same thing happen to your collection of gems?
Other than musicblocks and gems, what other collections are there?
Remember to make sure all of the items are in your inventory at the same time in order to get the trophy! Oh, and some collection achievements pay-off big time (especially the music blocks), so it's worth getting them!