Unfortunately, it does require a little luck to complete. It depends on how much Four decides to spam her shockwave attack, which is what will kill him or any ally that has to take on Psycho Gundam. As soon as Four show up, stop taking whatever field you're in, and pedal to her.

The best way to fight giant enemies is to charge up your Smash Attack and stick close enough to goad them into trying to attack you. Move out of the way, and if the green arrows that appear show up, hit 'em, and either fly up or dash back. They're gonna fall over, and the shockwave will knock you over and waste your time. Then just go hog wild on them.

You need to recognize the shockwave attack, which Four won't do until she's low on health. You can tell when she's gonna do it, cause the Gundam's joints glow purple. It's best is usually to pull back when she does it, but with Amuro standing his ground, you need to interrupt it. Just do the same as before, keep your Smash Attack charged, and hit when she's going to curl up. Don't worry about knocking her down now, just hit while you have the chance. You usually have enough time to recharge the Smash Attack, but don't worry about having to back off and let Amuro take a hit.