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Its not Legend 3. Don't recall that game having a giant bird in it.

Could also be Mystic Quest or FF:Legend 1, though Mystic Quest is pretty far from the standard FFs.

MOWLS2000 won't show up because its a re-release of Mia Hamm Soccer 64, not a unique game.

I'd wager the one you're looking for is one of the J-League games, probably J-League Tactics Soccer.

Might also be Chameleon Twist 1 or 2.

That sounds an awful lot like E-SWAT.

If its a horizontal shooter, it was quite likely Einhander you were playing.

First one kinda sounds like Dragon: The Bruce Lee Story

Was the shooter vertically scrolling or horizontally scrolling?

The platformer might be Super Adventure Island 2.

As was said before, it could have been from the Strikers series. It might also have been 19XX: The War Against Destiny. Same series, came out in 96 with a more modern approach to the franchise. Or...