All credit to go to Otaku1412 for their Marvel's Spider-man guide.
Story related, and cannot be missed. Your main focus should be on Hammerhead. When he brings out his minions, simply avoid them as Sable will take them out. You will get to know dodging well as if you get hit by Hammerhead more than once, he can take down your health in no time. Just keep at hitting his knees and eventually you will hold him while Sable fires at his head. Repeat this 3 times and he'll go into his second phase which includes adding shields.
Sable will do bombing runs and you'll have to throw the bombs to de-shield Hammerhead and then repeat the beatdown. His shields will regenerate if you take too long, so attack him as fast as possible. Repeat this twice more and that should finish him off.
The trophy pops after you get past the post-credit cutscene.