Okay, I've been testing this out, and Falco's not the only one who can do it. Fox can if he DOESN'T fast fall, and uses a dair to throw the shell down, then a uair or fair 2nd. If the second one is a bair or dair, you lose too much altitude.
The easiest way to do it is jump -> down C -> Forward C.
Also, this will work with ANY of Falco's aerials, including the nair. He can stay aerial as long as he want to, with any of them, though Dair is easiest because you've already done one to throw the shell down.
THESE ONLY WORK WITH GREEN SHELLS, NOT WITH OTHER ITEMS!!! It only works because you're landing on the shell just as you catch it, and it bounces you up.
I'll edit later if I find anything else out.
Edit:
Characters it will work for: (Moves listed indicates what to use after the first dair)
![Bowser :bowser2: :bowser2:](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)
Fair or Uair
![Wario :wario: :wario:](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)
Dair
:shiek: Anything except Dair
![Ganondorf :ganondorf: :ganondorf:](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)
Bair could work as a stall, but it slowly loses altitude
![Pit :pit: :pit:](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)
Any aerial
![R.O.B. :rob: :rob:](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)
Anything except Bair
![Dedede :dedede: :dedede:](/styles/default/xenforo/smilies/dedede.png)
They'll all work, but only Bair will keep you airborne forever. Even that one doesn't gain height.
![Fox :fox: :fox:](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)
Anything but bair or dair, don't fast fall.
![Falco :falco: :falco:](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)
Any aerial
![Wolf :wolf: :wolf:](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)
Anything but bair or nair, if he doesn't fast fall.
![Captain Falcon :falcon: :falcon:](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)
Any aerial. Not sure why, but if you do Dair -> Uair while your momentum is backwards through the air, you won't go up on that jump, just fast fall. You can still do more shell jumps if you get out of the lag before dying, though.
![Pikachu :pikachu2: :pikachu2:](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)
Nair and Uair work, but very slowly
![Charizard :charizard: :charizard:](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)
Fair and Bair work, but very slowly
![Marth :marth: :marth:](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)
Any aerial, but Dair will only stall, not climb
![Ike :ike: :ike:](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)
Bair will only stall, not climb
![Sonic :sonic: :sonic:](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)
Anything except Dair
Okay, so that's everybody that can do it. Of them all, Falco, Fox's and Pit's are by far the best and most maneuverable, but a lot of them get a surprising amount of use out of it.
Obviously, this has no tournament application, but I think it's cool nonetheless.