For grabbing GAME graphics on a real Amiga, Action Replay
(as Akira pointed out) is your best bet. Unfortunately many games use multiple overlayed screens, copper tricks, sprites, etc which the action replay can't always grab with its own function (at least not all on a single screen). I doubt that there are software screen grabbers that could grab screens any better either and they usually require a soft reset and for the user to physically search for each bitplane, colour map, etc.
If you want a game screenshot UAE is the most accurate (or at least as good as it is under emulation) because it saves each pixel as it exists on the emulated screen (as we see it), not as the graphics data is physically arranged in the Amigas memory.
If you want the captured screen to be displayed on the Amiga 1200 you could capture it in UAE, then copy the screenshot to the A1200 and show it with something like ViewTek in HAM8 mode.
Some games that do capture well with Action Replay are the Dragons Lair/Space Ace series. I captured many screens from those games and used them to create ANIM5 animations (it sure does take a long time though!).