Yeah, it seems I was quite off-mark These seemed to be the most reasonable ways at the time. Right now it looks something like that:
Unlockables seem to be tied to the number of times classic mode was cleared and perhaps to clearing it without continues, some may depend on intensity setting.
First three unlocks are Falco, Ness and Dark Pit.
10 Classics unlock DHD
Seems the next classic clear after unlocking DHD unlocks Mr. G&W
Link unlocks Ganondorf
Mario unlocks Dr. Mario
Lucina unlock doesn't make any sense, she seems to be unlocked after Mr. G&W though.
Wario is unlocked, well, somehow. Not tied to number of times classic is cleared as Gema unlocked him first.
Bowser does not unlock Bowser Jr. Note: maybe there is some other condition like clearing with all Mario characters or something like that. Update: GAF user GameFreak claims he unlocked him at 7.0 intensity. No pics yet.
Don't unlock anything: Ike, Samus, Lucario (I think?), Greninja, Bowser, Charizard (I think?)
Chorus Men are probably deconfirmed (Karate Joe trophy doesn't have a seperate Rhythm Tengoku icon)
Mii Fighters unlock when you make a Mii
New Classic Mode hidden boss - Master Core. It's insane. The higher the intensity the more phases it has.
More challenges unlock after initial page
Bonus: Wolf deconfirmed 100%, Squirtle and Ivysaur trophies spotted (duh), Isaac got seemingly demoted from AT