It's not that Godzilla: Destroy All Monsters Melee (Godzilla: Kaijuu Dairantou in Japan) is an especially bad game, it's just not very good. The fact that it's playable by 4 people at once, and has "Melee" in its title automatically brings frantic multiplayer battles to mind (ala Super Smash Bros. Melee) and this is the problem.
First of all the characters don't move very fluidly. "Far enough" you might think, after all they are big hulking behemoths. But the problem is it doesn't make for an enjoyable game. The characters attacks are too similar also. One character fire rocket, the other shoots a laser, they're both just similar ranged attacks.
Running around the city-stages can be fun, getting shot at by small tanks and destroying builings, but a lot of the time there's too many buildings and they obstruct you from having a proper fight.
If you love Godzilla, this game is probably pretty fun, but if you're just looking for another multiplayer game to play with your friends, try something else.