Text (ET): At the beginning of your upkeep, destroy target creature with a -1/-1 counter on it.
This ability is mandatory, so if you are the only player who controls a creature with a -1/-1 counter on it, you must target one of your own creatures. [Eventide FAQ 2008/07/08]
You choose the target at the beginning of upkeep and must choose something that already has a -1/-1 counter on it. This means you can't give something a -1/-1 counter during upkeep prior to choosing a target. [Eventide FAQ 2008/07/08]
The ability will be countered if the targeted creature no longer has a -1/-1 counter when the ability resolves. [Eventide FAQ 2008/07/08]