In order to get claim on a mob that someone else has hate on too (such as a mob that's been claimed but gone unclaimed, or someone else's aggro/link), you have to get to the top of the hate list, and then do something claim-worthy while still at the top.
If two people therefore alternate attacks, it'll go like this:
1. Mob has initial hate for A.
2. B hits mob. Mob has highest hate for B. B does not get claim, since mob previously had highest hate for A.
3. A hits mob. Mob has highest hate for A. A does not get claim, since mob previously had highest hate for B.
4. Alternate 2 and 3 until either a. the mob dies (in which case neither A nor B gets exp or drops, iirc), b. one of the players falls out of the equation by zoning or dying or just generating less hate by melee or something, c. either player fires off a claiming action (like hitting *again*, or voking, or something) while at the top of the hate list.