The Doctor Does Archery Now, Archery Is Cool
Even the famous archery competition is scheduled to happen the next day, where Robin will disguise himself to compete for an arrow made of gold. It's a trap, of course, but one Robin can't refuse -- after the sheriff shoots a bullseye, Robin wins the day by splitting his arrow clean through.
Where's the Doctor while this is happening? Practicing his archery skills (or archery trickery), apparently, as he shows up to split Robin's arrow in half. The sheriff then offers him the golden arrow, but the Doctor looks at it and tosses it aside, saying he wants something else: enlightenment. Though this seems to be the Doctor's main play to figure out just what's going on, he's interrupted by Robin, who splits the arrow again.
This farce continues with arrow after arrow until the Doctor decides it's getting silly -- though it's been pretty silly all episode -- and blows up the target with his sonic screwdriver. (Apparently, there's a setting for that.) It's been enough silliness for the sheriff, too, as he orders his guards to seize the Doctor. In the melee that follows, Robin winds up slicing off the arm of one of the guards and, surprising no one who read the episode title, the guard is a robot.
The Doctor is thrilled by this development, because now he's finally getting somewhere... so he surrenders, explaining the best way to figure out what's happening is to get captured. Clara and Robin apparently trust him enough to go with this which means the three of them wind up chained together in a dungeon... which leads to Robin and the Doctor bickering while Clara insists they need to come up with a plan.
Clara in Charge
Unfortunately for Clara, this means the guard listening at the door decides she's the one in charge and so takes her to the sheriff for interrogation. But because the sheriff intends to make her his consort once he's king, the interrogation takes place over a nice dinner, where the Sheriff answers more questions for Clara than she answers for him. His story is the standard Robin Hood tale up until the point where he saw lights in the sky -- a crashing ship, Clara guesses.
Will the Doctor come to her rescue? Well, without Clara, his argument with Robin has continued unabated. The two finally manage to come up with a plan for Robin to act sick to lure the guard in and knock him out -- but arguing over who will get the keys the guard's dropped leads to the keys getting kicked through a grate... so the two finally escape carrying the stone their chains are tied to.