This video covers both the MG Excelsus and Armstrong fight. I was hoping to get it all in one go with no restarts, but it'd been a while since I did these fights, so I ended up restarting once near the start of Excelsus because I messed up my combo and again near the start of the final phase for Armstrong for a similar reason. The requirements for Excelsus and Armstrong are as follows:
MG Excelsus:
Time: 8:00 for +2,000 BP.
BP: 800 for +2,000 BP.
Zandatsu: 2 for +2,000 BP (1 for +1,000 BP).
Longest Combo: 80 for +2000 BP (10 for +1,000 BP).
Kills: 4 (1 for +1,000 BP).
No Damage: +2,000 BP.
S Rank: 10,000 BP
Senator Armstrong:
Time: 5:00 for +2,000 BP (8:00 for +1,500 BP).
BP: 800 for +2,000 BP.
Zandatsu: 1 for +2,000 BP.
Longest Combo: 100 for +2,000 BP (10 for +1,000 BP).
Kills: 1 for +2,000 BP.
No Damage: +2,000 BP.
S Rank: 10,000 BP
For Excelsus, I ignore the 4 Kills since No Damage gives you 2,000 BP and you're guaranteed 1 Kill for 1,000 BP. For Zandatsu, I simply bait the cows into his laser attack and Zandatsu just before the next laser attack reaches me for I-frames. BP is fairly easy to get. Just get some good combos on his arms and legs.
Armstrong, while the last boss of the game, has pretty easy requirements for S-rank. While you're likely not going to get the 5-minute timer for 2,000 BP due to waiting out his 2nd Phase, you are guaranteed 4,000 BP just for beating him. 2,000 for Kill and 2,000 for Zandatsu.
This leaves us with Time, BP, Combo, and No Damage. Time is actually a null factor. You could get 0 BP from it and still get an S-rank. BP is easy. the 100 combo will already net you 100 BP and the Healing Pastes (4 of them) that drop from the debris after the Blade Mode section each give 100 BP each. I usually grab 6 of the Pastes since combos during the fight give me the rest of the BP needed. No Damage is, well, No Damage. Learn his attacks and what you can and can't parry/dodge.