This stage takes place on Disc 3 after you obtain the Mechat. It happens at the Upper Mecha Base, which is if you look at your world map, is the lower yellow plus symbol.
Unlike the other shooting stages damage to your Mechat does not matter here, to get Perfect, you must destroy all the machine guns on the base before completing it.
There are two parts to this fight:
Part 1: There are 4 pink discs that shoot missiles at you, destroy ONLY 3 of these as if you destroy the 4th the part will end before you can kill the machine guns. After killing 3 pink discs leave the other one alone and destroy all of the machine guns, there are 24 total in this section. After destroying all 24 machine guns go ahead and destroy the last pink missile launcher, then onto Part 2.
Part 2: Not to much different here. There will now be laser cannons near the middle of the structure destroy them as you pass by them, then destroy the machine guns found on each section, there are 4 per section. After destroying the cannons do as many laps around as you need to destroy the rest of the machine guns, the pink missile launchers left behind by the cannons are not necessary to take down and will respawn when you come back around to it.
After you are done blasting the machine guns, just pummel the middle mast and they stage is done.
The achievement will pop right after you destroy the mast, so if it doesn't pop up then you have missed a gun somewhere.