The spell or ability you target with Not of This World may have any number of targets, as long as one of them is a permanent you control.

Not of This World’s first ability checks the current state of the targets of the spell or ability it’s targeting to determine whether one of them is a permanent you control. For example, say a player casts Forked Bolt targeting you and a creature you control. If, in response, another spell or ability causes that creature to no longer be under your control, then you can’t cast Not of This World targeting Forked Bolt. Alternately, if you cast Not of This World targeting Forked Bolt and, in response, another spell or ability causes that creature to no longer be under your control, Not of This World will be countered when it tries to resolve for having an illegal target.

Not of This World’s second ability checks the current state of the targets of the spell or ability it’s targeting to determine whether one of them is a creature you control with power 7 or greater. This check is made as you cast Not of This World, before you activate mana abilities. It doesn’t matter what the power of the creature was at the time the targeted spell or ability was cast.

Not of This World doesn’t check whether the targets of the spell or ability it’s targeting are currently legal for that spell or ability, only who controls them and what their power is. For example, say a player casts Forked Bolt targeting you and a creature you control. If, in response, another spell or ability causes that creature to gain shroud, then you can still cast Not of This World targeting Forked Bolt.

If a spell or ability targets you, but not a permanent you control, you can’t cast Not of This World targeting it. Keep in mind that if a player casts a spell or activates an ability with the intent of dealing damage to a planeswalker you control, that spell or ability is actually targeting you, not that planeswalker.