This one's really not as hard as its TA score would suggest.
First you have to complete the four stages:
* Green Goblin: Shoot the ball up the Green Goblin ramp a few times, and GG will throw a pumpkin bomb onto the table. If GG flies to the left, shoot the pumpkin bomb up the lower webslinging ramp; if he stays put, send it up the Green Goblin ramp.
* Doctor Octopus: Hit the ball into the Doc Ock lock at the very top of the playfield (using the upper-right flipper). Doc Ock will try to walk down the table menacingly; shoot the ball into any of the webslinging ramps as many times as necessary to drive him back. The lower webslinging ramp feeds the left flipper, where you can hit it back into the same ramp again until Doc Ock gives up.
* Mysterio: Probably the hardest off the modes. To start it, hit the captive ball by Mysterio; he'll pop up somewhere else on the table, and you'll need to hit the ramp or hole he's hovering by to "find" him. Do that a few times, and the Mysterio stage starts. You have to hit the Doc Ock lock hole, the Mysterio webslinging ramp, and the Green Goblin ramp -- nothing too difficult, except that the flippers are backwards (left trigger controls right flipper and vice versa). As long as the stage is going, though, there's a ball save in effect, so there's not much pressure.
* J. Jonah Jameson -- Hit the right-middle orbit to activate. It's a 15-second hurry-up mode, you have to hit the right loop. If you're a good shot, you can get it immediately when the mode starts, since it drops the ball onto the left flipper.
Once that's done, put 4 balls in the Doc Ock ball lock. (The first ball lights the lock.) Once you get the last ball locked, the achievement pops...a 4-ball multiball mode starts, but you already have the achievement.
The biggest tip I can give for this achievement is: get the extra ball. It's so easy on this game. You just have to advance the Websling award three times. It's exactly what you did for the "Party Time" achievement -- you hit each websling ramp three times to advance the Websling Award. The third time you advance the Websling Award, it's an extra ball. Make this your first goal on every ball, then try to complete stages.