Green Lantern: Rise of the Manhunters

Go to upgrades under the start menu which will show all the upgrades you can purchase with your gained experience. The attack upgrades are the four at the top:

Buzz-Saw
Grab-Slam
Fast Attack
Strong Attack

Fast Attack and Strong Attack each have 3 different upgrade levels. You cannot unlock the 3rd upgrade level until your character reaches Level 8.

Once your character is Level 8, it is just a matter of gaining enough experience points to purchase them all.

This is gained by purchasing all the upgrades in the top row of upgrades that includes light and heavy attack upgrades which also have 2 more levels beyond the first, all of which you must purchase.