Goku's pretty sturdy against energy attacks so I'd wager that he can handle getting hit with a few blaster shots, but at this point I think his durability is low enough that he could be put down after getting repeatedly blasted. Roshi's lightning attack was enough to stop Goku when they fought around that time if I recall, so that's an approximate roof for what kind of energy attack takes him out- Which means if he starts out close enough to Palpatine for him to use force lightning, it's game over. He's also got no counter to being force-choked, which is a major hazard in fighting Vader.

On the other hand, it's a moon full of storm troopers fighting against a small, fast moving target with a magical weapon that I'd wager could withstand (but not deflect) blaster fire, since Goku still has his staff. They can barely land a shot on a full size Chewbacca, they don't have a chance of hitting a yoda-sized Saiyan. Unless someone gets insanely lucky, they aren't going to be able to stop him short of blowing whatever chunk of the Death Star he's currently in to oblivion and hoping the splash damage hits him.

For R1 the question is: How long can kid Goku fight without rest? There's appx 1.7 million personnel on the Death Star, spread across a moon-sized station. Goku can't exactly stop and take a nap because that'd guarantee they get the drop on him, at which point he'd need to keep fighting to stay alive. Eventually either he runs out of targets, or he succumbs to exhaustion.

R2 has the same problem, but now with a major opponent. If Vader gets a force-grip of him, then it's game over. If Goku manages to charge and fire off a kamehameha then that should be fast enough and powerful enough to take down Vader (assuming we're going off the movie version here).

R3: Same as R2 but swap Vader for Palpatine and add in force lightning.

I think Goku clears R1 fairly well, albeit with some major exhaustion by the end. His opponents on their own aren't that impressive, but there's a lot of them across a wide distance to hunt down. R2 is where he stops, against Vader he either lands a perfect kamehameha or else Vader overtakes him through his mastery of the force. Same for Palpatine.