Even after the curse was lifted in the first movie, Barbosa's monkey Jack remains undead.
In Dead Man's chest, Jack trades the monkey with the witch and shot him and pronounced him as undead.
How is that possible?
After the death of Barbossa(ending of curse of the black pearl) Jack(monkey) took a coin from the chest getting himself cursed again,similarly to what Captain Jack Sparrow did during the first fight.
Sparrow had a reason for taking the coin Jack on the other hand didn't...but he is a monkey afterall :/
Have you watched the after credit scene in the first film? That's where the monkey steels another coin.