A little less than half, I'd say, but I reset recently. Although I've never completed my museum on the other files either, I'm the worst when it comes to diving... some of those critters are just too fast for me.
I finished with the fossils last year, also the bugs and fish. Only need a few more paintings.. (This is only in my main town, my other town, Moonview is no where near done and I need to buy a new game for my other town Chocolat )
Mine is sooooo empty. I almost filled it up before and on my current playthrough it isn't that big a deal anymore, at least I still give him art and the bugs and fish and stuff that I promptly sell show up in the encyclopedia.