Chris Redfield vs. Wesker.
Grab a friend to do an Xbox LIVE match. One person selects Chris Redfield in their team while the other selects Wesker as one of their members, then play the match.
Can be obtained through Ranked, Player, and/or Private Matches. Doesn't matter which order you pick your character just as long as your opponent has the rival character. Both players will unlock the achievement after the match.
Furthermore, using Jill against the two will not unlock the achievement. (Credit to sourtart)