NY Warriors (aka New York Warriors) is a top-down shooter for 2 players developed by Synergistic and published by Virgin Games in 1990. The game was released for Amiga, Amstrad CPC, DOS, and ZX Spectrum.
If you take two arcades, such as Ikari Warriors and Commando, and mix them with the famous movie Escape from New York, you have a clear idea about what the developers wanted to accomplish. You have terrorists from the future, a dystopic world, distorted guitar music, bullets flying everywhere. And of course, 2-players simultaneous mode in co-op, for maximum fun. The graphics are not exactly top-notch, probably a bit amateurish, but this does not affect the gameplay. We are not at the levels of the arcades mentioned above, but considering that the Amiga port of Ikari Warriors was not exactly a masterpiece, NY Warriors is a good alternative. Bullets, explosions, and guitar, what else do you need?