How do I catch the bird that's in the tree?

You'll need to scare the bird out of its resting place first.

The Warrior can punch the bird and it will fly up.  Notice where it goes.

Through one of the holes at the top of the tree.

Too bad that there are two holes; if there were only one, you could figure
out where the bird would go.

So put the cork in one of the holes at the top (it doesn't matter which).

Now that you know where the bird is going to go, you can prepare yourself.

Remember that butterfly you were trying to catch?  The same trick will work
on birds.