Let's check your sentence and make it clear and easy to understand! Your sentence is:
"a cockatoo looking out of the page edge or a branch to really show its pretty crest up close."
To make it a complete and correct sentence, we can say:
"A cockatoo looking out from the edge of the page or from a branch to show its pretty crest up close."
This means the cockatoo is peeking out either from the page or sitting on a branch, and we can see its beautiful crest (the feathers on its head) up close.
Remember to start sentences with a capital letter and include a verb to show the action!