After you take out the big bad large Vajra in the 3rd wave, hang out with the small fry until your SP fully refills. Take out the little guys, switch to Fighter, fire off HM missiles at Brera while charging at him, when you get close switch to Battroid, then SP dash until you're right in his face, then immediately SP melee and you should take out a good chunk from him. If you have enough SP repeat, if not, gtfo of there and go back to the missile strategy until he's gone. If you hurt him bad enough (a decent SP melee blow should leave him pretty low on HP), he'll turn tail & be easy pickin's for missiles or more SP melee.
Providfed Alto survives through the ordeal, you should S rank it. If Alto survives and your HP is high enough, you'll SS it.
Interesting note, I'm playing through the game again with the pilots I didn't choose the first time (since I didn't get the all pilot skill & all pilot hearts titles, which I STILL haven't gotten), and in doing so went through all the stages in order. It wasn't beating Sad Sniper with an S that unlocks the VF-27, Battle Frontier, & Brera, since I did that in stage order. It was doing that in addition to finishing all other stages that unlocks them, since all of that unlocked once I finished up the Frontier campaign.