PSX SRW Gameshark Codes (Skip Animations)
Super Robot Wars F/FF
Super Robot Wars Complete Box (works on all 3 games)
Super Robot Wars 4S
Shin Super Robot Wars (don't fire MAP weapons with this code on - it hangs the game)
Shin Super Robot Wars (if the code above doesn't work. The game has two versions)
The way those codes work is like this: they're actually Debug Mode codes, and the last two digits represent which of the debug functions you would like to turn on. 00 turns Debug Mode off, and FF turns all debug functions on. If you just want to skip animations, then enter 40 as the last two digits. One warning: those codes are actually saved together with your save game (if you save after entering the code), so you don't need to enter them everytime you play. Just save once with the code on and it'll stay for the rest of the game. Another thing: there's no onscreen indicator of damage dealt/received, like in Alpha. You'll have to look at your/the enemy's status to see how much damage was done.
If you want to play around with debug mode, those are the codes I've found:
00 - turn all debug functions off
08 - ??? . IIRC, it either gives you infinite movements or lets you control enemies (if it isn't this one, then it's 10)
40 - Skip animations
48 - Infinite Movements per turn AND Skip animations
FF - All debug functions on. IIRC, if you press SELECT during gameplay, you'll get the Debug Menu. It's all in Japanese.
If you saved with any of those codes and want the game to go back to "normal", enter 00 as the last 2 digits and save your game.