There are 3 basic ways to destroy a character (I hope I'm not forgetting any).
1. Fatal damage - This is when the character has at least 1 damage on them and that amount of damage is equal to or greater than their health. Allies with fatal damage are destroyed during pre-priority processing. This is the kind of destruction that Gift of Nature stops.
2. 0 health - If a character's health is reduced to 0, they will be destroyed during pre-priority processing. Gift of Nature does not stop this.
3. Direct destruction - Whenever a card tells you to outright destroy a character you do that when the link resolves. You don't wait for pre-priority processing. This is what Kedryn is doing and Gift of Nature does not stop it. In fact, that's what Gift of Nature's second power is doing.
4. Physically rip up the card. (While this form of destruction won't actually affect the character in question as far as the game goes, it's pretty much guaranteed to get a rise out of your opponent)
4th Place, Day 1 US Continentals 2008 (22nd place overall)
1st Place, Ashenvale Realm Champs 2008
1st Place, Seattle Regionals (7/5/08)
1st Place, Seattle Regionals (5/31/08)
1st Place, Spectral Safari (3/1/08)
1st Place, Seattle Regionals (1/12/08)