Well, if Princess Peach starts hostile to him, he has almost no chance. Her speed & reactions are so much better that anything he does she can notice, she can react to in a miniscule fraction of time. Meaning before Tai Lung could finish any approach, she could be at his throat, & slap him to the floor. (Among numerous other ways of speed blitzing &/or one-shotting him.)
But at her most incompetent/Plot-Induced-Stupidity Laden, Princess Peach is very able to be incapacitated, & unlikely to fight back. If Peach were like that, he could certainly capture her to incapacitate her. If she can spend whole games like New Super Mario Bros. not breaking out of ropes tied around her waist, similar may work for Tai Lung.
& if Tai Lung WEREN'T so overconfident, & they were introduced in a non-hostile situation, where he knew he had to defeat her, he might be able to win, actually.
"Hello, your majesty, Princess Peach. I am Tai Lung, a great martial artist who seeks to become the Dragon Warrior." Tai Lung walks to Princess Peach, maybe kneels, & then offers a handshake.
"Pleased to make your acquaintance." Princess Peach accepts the handshake, as it's the polite & royal thing to do, & if she's not hostile to him, why not?
With her hand & perhaps wrist now literally in his grasp, Tai Lung COULD use his Pressure Points & Paralysis Inducement. If it works, she's paralyzed & incapacitated, & the surprise may give him enough time before she realizes to take action to paralyze the rest of her body, assuming a hit on her hand/wrist isn't enough to stop the rest of her.
But of course, that requires a hostile & perhaps uncharacteristically humble Tai Lung (As opposed to him being overconfident & outraged at the idea he couldn't beat a princess in an actual fight.) facing a non-hostile Princess Peach, & even in such a situation, there's a chance of failure.
But sure, it's possible, lol.