Surprisingly, I was able to dig up some pretty good information. Your ancestor, Richard Waller, was the son of an esquire at the time of Agincourt and served as a man-at-arms in the company of Captain William Bowes. William Bowes' company was made up of a total of 33 men, 10 men-at-arms and 23 archers, and served under the command of the Duke of Clarence. The Duke of Clarence at that time was Thomas of Lancaster, Henry V's younger brother. So your ancestor was of fairly high status, and belonged to a fairly high status unit. His role in combat would be to dismount and stand in formation with the other men-at-arms and knights, protecting the archers from the French heavy infantry. He was obviously stationed somewhere that saw the thickest fighting, because the Duke of Orleans was commanding the French vanguard and lead the assault. Capturing him would mean taking on some of the most capable and best equipped men-at-arms present in the French ranks.

The Duke of Orleans was only twenty, the nephew of King Charles VI of France, and had never fought in a true war before. However, he does seem to have been a capable jouster and skilled in arms despite his inexperience. The sources I'm looking aren't entirely clear on whether Richard Waller personally took down the Duke or whether he just found him under a pile of dead bodies. However, Waller is mentioned as being accompanied by a group of archers from his unit. After running out of arrows, they had dropped their bows and drawn weapons to fight in close combat. Waller, as a heavily armored man-at-arms, would have engaged a French soldier, then the lightly armored archers would sward around his flanks to overwhelm their opponent. Fighting as a team like this, they were very capable of handling even the highest quality French knights, like those who would have been fighting alongside the Duke of Orleans. Waller captured the Duke and handed custody of his royal prisoner to King Henry V. Upon the army's return to England, Henry V gave the Duke back to Waller for Waller to house and feed. This turned out to be a generous move, because the Duke generously paid for not only Waller's new manor, but also repairs for the local church in Splendhurst. Waller, now able to call himself Sir Waller, commemorated his good fortune by adding an image of the Duke's shield to Waller's own family arms, a walnut tree. The hilarious caption on this new coat of arms read Hœ fructus virtutis or "This is the fruit of valour." The Duke spent twenty five years as a captive in England (but didn't spend that entire time in Waller's care), and became well known for his poetry while he whiled away the decades.