I think you need a lot more than 21 to make it to Eagle. Are you sure that's not 21 more to go from Life to Eagle, on top of all the badges that have to be earned to go from First Class to Star, and from Star to Life? I had to earn 5 just to get to Tenderfoot from Scout and then 10 more to get to Second Class. After that comes First Class, Star, Life, and Eagle--never made it to First Class. I'm sure the cumulative total of merit badges you have to earn to get to Eagle is huge.
I did have one of the ones that would eventually have been required for Eagle, at least according to the modern requirements: Cycling. Probably the easiest one of the bunch. But like I said, I never made it as far as First Class, and I do know you can't skip ranks.
This was many years ago, more than I'm going to admit to--maybe things have changed?
I made Eagle Scout in Sept. 1970, one month before my 14th birthday. They've changed the merit badge requirements since my day -- going on memory here, but as I recall 11 of 21 were required -- Swimming, Nature, Conservation of Natural Resources, Citizenship in the Community, Citizenship in the Nation, Camping, Cooking, First Aid, Safety, Personal Fitness, and the big one -- a real showstopper for a lot of Scouts in my day -- Lifesaving. I remember my Lifesaving course -- out of 15 people taking it, 10 failed it. It was a real bitch.
I wound up with 26, qualifying for a bronze palm.
They've changed a few of the required badges and gave options where previously there were no options. Lifesaving OR Emergency Preparedness (WTF is THAT?); Personal Management; Environmental Science; Family Life (yeah, all about the birds 'n bees); and Communications replacing Cooking, Safety, Conservation of Natural Resources, and Nature.
I failed my first board of review because my service project, which I'd already completed, wasn't approved. Nobody bothered to tell me that somebody had to approve the damned thing. So I had to do another one.
Meh. It didn't kill me.

On a more shitty note, all my Scout stuff was "inherited" by the State of Michigan when my Dad died. No idea where that stuff went and no chance to get it since the State wound up with the house.