-( Story related, cannot be missed )-
Axiom City was a pain on my first playthrough, but this boss took the cake. The first stage of the fight has you standing before it, getting ready to laze the place up. Simply let the conversations proceed (Azimuth just gabbing on about distracting it, yada-yada) and the VX-99 will proceed closer to you. By the time it gets within range, Azimuth will unleash a barrage of shots onto the machine, which will spread its metal skirt.
Jump onto the skirt to start the second stage of the fight. You will have to avoid the lasers three times while dismantling the arms that are shooting the lasers. Simply make a run up and down, avoiding the lasers even when they begin to rotate around. Eventually, the gears will be exposed and you will need to use your wrench to tear the leg off, which will destroy the skirt as well. Repeat this two more times and you will be thrown up onto the head plate for the third stage of the fight.
This stage simply has three joints holding the head case to the platform, with rotating lasers trying to challenge you. Use L2 to strafe and either unleash an assail of ammo, or use your wrench. Either way, jump to avoid the lasers as they sway back and forth to try and stop you. Once you've completely destroyed all three gears, it will leave big enough cracks for Azimuth to break the glass completely.
What will be left is the main unit of the VX-99: the head. From here, just keep drilling it full of ammunition and it should go down simple enough. I don't remember having much difficulty with this monster once I got to this stage.