Do (one) in the eye verb phrase
To trick, thwart or humiliate someone
I didn't mean to do her in the eye in front of her friends.
When I was about to tell my boss my idea, John did me in the eye. We haven't talked to each other since then.
To have a blush on the face, especially when one are embarrassed
1. To shame someone/something.
2. To achieve better results than someone/something.
The verb "do" must be conjugated according to its tense.
The origin of this phrase is not clear.
If you swallow the bait, you take something that someone offers you, or agree to do something that someone asks you to do without knowing that it is a trick or way of getting something from you.
You can't just do whatever he wants you to do. Don't swallow the bait.