The Hunters
You'll be dragged back up to the city. You'll have to fight a hunter which is a very fast moving robot that flies through the air. You'll have to close in on the Hunter and use a Web Strike on him to deal damage. After you've dealt damage this way, the Hunter will take off again.
When you get close to it this second time, it will activate an electric bomb with it at the center. First it will charge up and deal a little bit of damage as long as you are in the field and then it will release the energy for massive damage. You can die from both parts of this attack (though the second stage is far more deadly) so it's important that you escape as soon as it happens. I highly recommend that you use Web Rush instead of Web Retreat because it's very easy to keep bumping into buildings with Web Rush and not make it far enough away.
After it uses that Electric Bomb, you will be able to get close and use a Web Strike. After the Web Strike, when you get close it will use the Electric Bomb and this cycle will continue until it's defeated.
It also has a plasma ball attack. It will shoot little balls of energy at you very quickly. You can definitely dodge these but you likely won't have to put too much effort into dodging as long as you keep moving.
To get close, you have to techniques to your advantage. The first are your web shooters. This will slow him down significantly but is unnecessary and (for this fight) not recommended. You also need to use Web Rush instead of swinging because it's much faster. There's an achievement for defeating a Hunter without using Web Shooters so we're going to try that. Just keep hitting the Web Rush button until you execute a Web Strike on him instead. Once you do, get close and make him trigger his electric bomb. Escape the bomb and then continue your chase.
One thing to keep in mind is that when you use Web Rush this much during a Hunter battle, it's important to move left and right as much as possible since your elevation isn't going to change much and you can easily (accidentally) move in a straight line for a long period.
Once the hunter goes down, two more will appear. In some ways, this is actually easier than the first Hunter because you can move between them quite easily with the Web Rush. Just pursue them and you'll find that you are almost constantly chasing and using Web Strike on each of them while the other is trying to use it's bomb attack.
When you get past the first Hunter, you'll actually reach a checkpoint so if you die, it's ok. Just keep trying and once you get the hang of it, you'll find that Hunters are quite easy and even kind of fun.
*Achievement: Who's the Prey?
*Achievement: Clean Victory