Ow come on, maybe he didn't linked the name "Beast" to "Shadow of the Beast"
For shoot'em ups, go for Apidya, Uridium 2 and Battle Squadron. Those , IMO, are the best of the genre.
The Amiga is full of great platform games, here goes a few you could try:
James Pond 2
Other games you HAVE to get, imo:
Sensible World of Soccer, Brutal Sports Football, All Terrain Race, Cannon Fodder, Alien Breed 2 and Alien Breed Tower Assault, The Chaos Engine..
Hmm.. it's 5:30 am now, I can't think very clearly
I'tl try to remember a few more later.
I see you've changed your avatar, huh??