Corrected sentence:
With its pointy beak, the woodpecker can peck a hole in a tree for its nest.
Why this is better (easy steps):
- The phrase "With its pointy beak" is an introductory phrase, so we put a comma after it.
- We use the verb "peck" because woodpeckers peck at trees with their beaks.
- "A hole in a tree" sounds clearer than "a tree hole."
- "For its nest" tells why the woodpecker makes the hole, and that is fine. You can also say "to make a nest."
Another short version: The woodpecker pecks a hole in a tree with its pointy beak to make a nest.