In The Amazing Spider-Man for the PS3 and Xbox 360, there is an easy way to level up your skills near the beginning of the game by investing a little time.
In the “Oscorp is your Friend” mission in Chapter One, you will fight your first S-01. Killing an S-01 will net you 2,000 experience, and 150 tech points. Even though it takes a couple minutes to beat one, you can save your game and continue to beat it as many times as you want to gain a lot of experience and tech points.
