to think of oneself as cat’s whiskers = to be big-headed, to regard oneself as important
I can’t stand him. He thinks he’s the cat’s whiskers.
in the catbird seat = to be in an enviable position, to have an advantage
He was in the catbird seat being in charge of the project.
to grin like a Cheshire cat = to have a wide smile
“The prize is mine” he said, grinning like a Cheshire cat.
cat’s eyes – retroreflective safety device on the roads
like the cat that got the cream = very pleased with themselves, happy about one’s achievements
Mary has just passed the exam with flying colours. No wonder she looks like the cat that got the cream.