This quest can get complicated with the clock ticking. May take a few attempts but it's possible. You'll need to bust a caragor out of their cage and then break them before mounting them. I recommend using your bow if your level isn't up yet.

You'll need to kill 7 Orcs while mounted, so be sure not to let your caragor fall in battle. This was the case for me during my first play through. Fortunately for me, another caragor was immediately available. Don't hesitate to use your bow if your caragor energy is running low. Give some distance between you and the captains to prevent from getting overwhelmed.

For the end battle where you have to defeat 15 enemies that includes 3 captains and a Nazgul. When overwhelmed it is difficult to drain orcs for health so I jump to the top of the towers and try to lose their attention. Once they've lost me, I flank a single orc and stealth drain. Filling my energy and continuing the battle.