There are 2 versions of this game:
1) Arcade, PC, PS1 & Saturn (1996, developed by Iguana)
(^arcade)
2) PC, Genesis, SNES, Game Boy, & Game Gear (1995, developed by Probe)
(^SNES, courtesy of supernesroms.net)
1-2 players(handheld versions most likely only 1 player)
Probe controls:
https://www.gamefaqs.com/genesis/366838-batman-forever/faqs/31958
https://www.gamefaqs.com/snes/588208-batman-forever/faqs/29217
(if these don't give you the gist for GB and GG, well you'd most likely rather play the 16-bit console versions if you're going to bother anyway)
The 16-bit/console version of the game has adventure elements, as you try to figure out what the Riddlers clues mean, while looking for hidden areas in the stages. It also has a fighting game mode where you can play as any enemy in the game. The 8-bit/handheld version is more straightforward.
Iguana controls(arcade version, shouldn't be hard to figure out the others from here):
button 1 - ???(possibly only used for name/initial input)
button 2 - jump
button 3 - punch/items
button 4 - kick
3, 4 - jump kick
walk into enemy, grab
grab, 1 - strike combo
grab, Left/Right & 1 - throw
grab, Up & 1 - throw into background
You collect various power-ups, bat symbols increase a bar underneath the health that does a full screen attack, and bat weapons have limited use, but you won't get the punch back until you do. Sometimes there are Riddler icons that have various effects, like shrinking Batman/Robin or their enemies. There's sprite scaling as you walk Up/Down the planes. It's a very fast paced game(almost like an acid trip at times), so you need to be careful you're not on the receiving end of an enemies combo that you can't recover from.