The Amazing Spider-Man

Edit: This is my way of doing this achievement, but it is by no means the only way.
For this method you have to unlock the web hurricane ability. You will get this ability fairly late in the game. This allows you to web attack someone and press B and instead of hitting them, you will land and release a large mass of webbing to tie up nearby enemies. This can be done after only purchasing one level, but if you are having trouble, there is a second tier of this upgrade.
The easiest way to get this achievement once you have this ability it to load up the metal hospital where you rescue Conners at the very start of the game. Very near the start, there will be a group of six patients you have to fight. Simply stand there and wait for them to group around you, then press LB to escape and they will stay where they are. If they are grouped close enough together, use the RB to web attack and as soon as you let go, press B and when you land, you will web up all nearby enemies. If you dont get all six, try again.
Note: Do not counter attack, just take the hits the patients throw out and escape to heal or you may kill one of them.

If you follow Dauntless's way it works just fine. Tried it out for myself and success. If you need a video for that I found one done by the Achievement Hunter community.

Spider-Man, Keep It Together Achievement
- Immobilize 6 enemies simultaneously with web.

You can immobilise enemies (wrap them in web) in a number of ways but the easiest is just to mash B until they are surrounded in web.

Despite what is said in the other solution you don’t 'need' any upgrade to get this and it can be obtained as early as mission 2 - though I recommend getting the Web-Strength upgrades to increase the amount of time enemies stay immobilised.

So to get the achievement just start mission 2 and as soon as you encounter enemies (a bunch of about 10 escaped patients) simply run around and mash B until it unlocks. The game automatically switches targeting to an unwrapped enemy when your target is immobilised so you really can just mash away - it is just that easy.

I am going to tell you the easiest way to gain this achievement without destroying your "B" button on your controller

*SPOILER* On the last level when you are looking for Croc in the sewer, you will eventually run into a room when Gwen is on top of a Spider Hunter fighting off some enemies.

First, take out all the spitting enemies on the ledge (they are the one big orange overalls wearing guys). Once they are knocked out, let the baddies gather more and more around Gwen and the Spider Hunter till you can count six or more (best way to do that is to slow down time with Web Rush). Once there are six or more around her, Web Rush to one of the baddies and do Web Hurricane (Web Rush and then hit the "B" button once). This will cover all the enemies in the area in webbing and the achievement should pop.

Just trying to keep your "B" button alive on your controller.

All solutions above were great but just in case you were wondering the earliest you can get this upgrade, I used the 15th upgrade point I unlocked, so I guess it means you have to be at LEAST level 15 or 16 to get it.... You maybe able to get it earlier in the game story line by replaying levels, due to the fact that upgrade points seem to be given by leveling up......it became available I believe the same time the web punch was available,, I only saw it AFTER I'd already put the first point into web-punch