Original sentence: A mandrill’s face has so many colors, it’s like it’s wearing makeup.
Corrected sentence: A mandrill's face has so many colors that it looks like it's wearing makeup.
Why this is better (easy steps):
- mandrill's is correct: it shows the face belongs to the mandrill.
- Using that (or a semicolon) makes the two parts fit together more smoothly than a comma.
- it's means "it is" — so "it's wearing makeup" = "it is wearing makeup."
Short answer: Your sentence was okay, but the corrected version sounds a little smoother.