Some spells, such as Voodoo Queen (Water Magic), give you a chance to Curse a monster. 

When a monster is Cursed, it turns purple. A voodoo doll and a turn counter appear in front of it.  The counter shows how many times you can draw a card before the Cursing effect ends.

To complete a challenge that asks you to “defeat X Cursed monster", you must kill a total of X monsters WHILE they are still Cursed. 

Note: If the monster is no longer cursed when defeated, then it WON'T count toward the challenge.

Learn more about: How do I Curse a monster?