Okay, so this wasn't the first martial arts fighting game of the 1980's, but it was far better than both Karate Champ and Kung Fu Master which were released in 1984.
Featuring gorgeous character animation and digitized speech, combined with a wide variety of moves (very realistic they were, too) this was almost the perfect beat-em-up in the mid eighties. In fact, this game set the standard for this type of game, and surely influenced many games that followed such as International Karate.
The game was first developed for the C64, and then ported to other systems including the Amstrad CPC, Spectrum, BBC Micro, Acorn Electron and Commodore 16. Karate champion Jeoffrey Thompson was signed to promote the game, although he wasn't well-known enough to have his name used in the title! A bonus round where the player is charged by a bull never made it to earlier C64 versions or the Spectrum version.