How a could a 78-year-old (going by Clint Eastwood's age at the time, which we can assume corresponds to Walt) man beat up a teenager? Granted, said teenager was hardly in peak physical condition, and Walt took him by surprise, but it still seems like a stretch, considering the other action sequences in the film are handled other much more plausibly; in the scene where Walt smashes the cabinets, for example, it clearly takes a lot out of him, and his knuckles are bruised and bleeding, and when Thao trips him in the garage, he takes the fall pretty hard. So why attempt to show Walt as capable of beating someone up when up until this point he's been portrayed as about as agile and strong as you would expect someone of his age and physique to be?
An elderly war veteran beating the shit out of a much younger criminal is not unheard of. Soldiers are trained to fight. Criminals (generally) are not. And training counts for a lot in a fight. As for the rest, his hands were bruised and bleeding after smashing the cabinets because he was beating his knuckles against wood and glass, not flesh. It's also not surprising that a fall on the concrete floor of his garage took a lot out of him. Concrete hurts. Just because Walt can throw a punch doesn't mean he can take a lot of punishment, especially at his age.
He did seem quite tired after administering the beating.