Spider-Man 3

For this achievement you need to complete all the combat tours. There are 10 combat tours. Three easy ones, three medium ones and four hard ones. You fight the three streetgangs on each tour.When you finish an easy one, an medium one will unlock etc etc.
The object is to complete the tour within 10 minutes. You can get bronze/silver/gold times for this but there isn't an achievement for that so don't worry. After 10 minutes the mission will fail.
For all of these tours use the black spiderman. I did that and it worked much better then the red suit because the black one can use rage. Just beat up a thug untill your rage meter is full and use your powerslam (press A and while mid air press Y+RB) and you'll knock the groups away, save time and don't get hurt.
Another thing I found out is when you find all the collectibles for the streetgangs you'll unlock an ability which lets you do more damage against that specific gang. For example find all Apocalypse tokens and you'll do more damage against all Apocalypse gang members. This is an passive ability (much like improved health etc) so you don't have to activate it.
WARNING: Play all the missions with one Spider-Man suit. Appearantly the black and red suit have different saves (Don't know the reason why) but when you complete one tour with the black suit, it doesn't show complete when you'll switch to the red suit. Maybe it still counts for the achievement but in the worse case you'll have to do it again with the other suit so get them all in one save (all on black or all with the red suit) The same goes for the ability granted for finding all of the tokens.
Hope this helps. Good luck.

I never needed to get the extra damage to beat these fairly easily. As McD76 said, you should use the black suit and the power slam (once the spider symbol is full- filled by doing combos- jump in the air and press Y and RB).
A great way to take care of most enemies is web yank them into the air by jumping and pressing B, then beating them in an air combo.
This does not work on Dragon Tale gang members with swords and does not work well on the Arsenic Candy members that have mallets.
You can also web yank enemies over water and drop them for an instant kill. I like to lure nearby groups over to the water and take out numerous foes quickly this way.
For the harder enemies, those with mallets and swords, save them as the last enemies of each group and take them out with relentless ground combos. It greatly helps to fight them in slo-mo by holding down the LB.