It is determined by placement on the "top attacker" list, even though that's a bit of a misnomer since it's a combination of the different factors mentioned in the post. You need to get on that list only once, in any position, and you get one reward per character.
@Kyronix So to get a prize in Part V, you have to kill the Titans... How many Titans? How many prize choices can you get on a character? Will the prizes be awarded on a curve, a la the Gargoyle Cure? (please say no, nobody felt good after that event ended) Is it the title plus one or more of the other choices?