Does the "Alternate Reality" Crisis require each player to destroy 12 cost worth of Heroes?
Turns out that this is actually answered in the Specific Card Clarifications section of the Crisis rulebook:


  Alternate Reality, Final Countdown: To beat one of these Crisis cards, the team acts together and chooses which cards to destroy. The burden is on the collective team, so each player does not destroy their own set of cards to beat the Crisis. For Alternate Reality, you don't have to destroy exactly 12 cost worth of Heroes to beat it.


As it clearly says, "each player does not destroy their own set of cards" and it's up to the team to pick and choose which cards from which discard piles to destroy so that the total is 12 (or more) points of Heroes.