Story related, unmissable.
Obtained after beating Vermin during Chapter 3: The Thrill of the Hunt.
During the first fight with Vermin, you can pound on him with combos whenever you like, as long as you dodge his attacks with when your spider-sense triggers. As the fight progresses, he may disappear into the acid around you and leap out somewhere else, but if you keep moving, you won’t need to worry too much. Web strike him with when he starts doing this and you can continue your barrage of punches until he goes down.
Unfortunately, this won’t unlock the trophy, since you will need to follow him through the streets of New York and through another sewer section first.
When you catch up to him again, the fight is basically the same as last time. However, keep moving, because the rats on the floor can do a lot of damage to you if you stay in one place for too long. Repeat the same tactics as the first fight with the ratty menace, and you’ll beat him easily and unlock this trophy.