And his efforts will need to be thwarted, as the fulfillment of his goals directly preclude the objectives of the party from being met. That is understood, as is the likelyhood that Psimax may need to be killed. If such is necessary or advantageous, then by all means they should proceed to do so. If it is neither, then the party would essentially be killing him for excrements and merryments, which is neither Good, Heroic, nor particularly smart.
Hatred, though, is not very likely to be conducive to success in either case. While it may give determination and drive to minions, strong emotions can interfere with the cool head and cold calculations necessary for decision making on the higher levels. And we saw what happened with Forgath's frontal assault against Psimax; barring a deus ex machina, the party will need to act smart with this one, rather than blindly charge and get creamed.
People in love do stupid things. People who hate can do so as well, as the single-mindedness clouding their judgment makes it more likely that they'll miss something, and slip up. In the heat of passion, it is easy for people to do things they'll later regret.
You should not desire the death of Psimax as anything more then a means to an end. But if you do, then I think the best thing to do would be to take a deep breath, clear your mind of strong emotions, and then start plotting his gruesome demise.