Defeat a boss on any difficulty level without taking damage
On any boss encounter where you fight a main enemy (the enemy the level is named after), you must not take any damage. If you refill your health, that doesn't count. One of the easiest early fights is the first encounter with Hobgoblin. Hold to keep locked on to him. When he throws a bomb at you press to catch it, then again to throw it at him. When he falls, use the attack to damage him severely. Make sure you always dodge his gust attack when he uses it. It's very easy to dodge. When he gets out two bombs, you'll want to press to shoot some web at him which will make him drop both and a lot of times damage him and make him fall where you can finish him off. There are other boss encounters to do it on as well if you want as long as you learn the boss's attacks.
Note: You can reload your checkpoint on a boss encounter if you get hit.
This doesn't mean that you have to go through the whole boss fight without getting hit, but only one part of the battle. The easiest way to get this is: 1. Buy the "Web Shots" ability; 2. Play the "Hobgoblin" level; 3. At the beginning of the level stand ALL THE WAY BACK; 4. When he tries to throw the bomb, shoot him with the web ball (RB); 5. Repeat step 4; 6. Grab him when there's B displayed over Hobgoblins head. 7. Voila!
You can get this during the last battle with Mysterio as the Spider-Man Noir character. All you have to do is sneak your way towards Mysterio without being spotted. If you do get spotted, you'll get blasted by a big force ball. Once you do this and attack Mysterio at the end, you'll receive this achievement.