Go to the Duke's Audience Chamber and talk to Aldous, after completing his first round of quests. Choose to assist Ser Mercedes. Accept his request to accompany Ser Mercedes on her task.

This begins the quest:

Pride Before a Fall
Speak with Mercedes

Objective
Royal Orders Quest
Mercedes is determined to undertake a mission under the Royal Orders. Look after her safety.

Details
Talk to Mercedes to discern her motives.

You will find Mercedes near the castle gate. Talk to her. She tells you about dark happenings at the Stone of the North - Lord Julien's watch. He set out for the hold himself some time ago, but there has been no word since. Then, you need to travel to Windbluff Tower. This is NOT an escort mission, you travel there yourself, you don't have to wait for Mercedes. To get there, follow the road Northwest, cross the bridge, and then continue to the Northeast. When you get there, a battle is going on. Seek out Mercedes. Climb the stairs on the east side of the hold, and follow Mercedes in. Watch the cinematics.

You now have a choice:

Watch the Duel (Default Ending)
Observe the Duel. Ser Mercedes insists you do not intervene.

Reward: Mercedes gives you a Silver Rapier

Alternate ending #1
You could ignore Ser Mercedes request to stay out of it, and instead attack Julien. You should have no problem defeating Julien.

Reward: Mercedes gives you a Cutlass (But Silver Rapier is better)

Alternate Ending #2
After killing Julien, you can use a Wakestone on him to revive him (do this immediately after the cutscene). He admits his defeat and agrees to return to the capital and put himself to the mercy of the court.

Reward: Talk to Julien again in Gran Soren. He gives you his shield, the Wizard's Vizard (A very good shield). You also get the Cutlass from Mercedes

The shield is the best reward in my opinion, so you should go for that ending, unless you really want the Silver Rapier.

After the duel is over, report back to Aldous.

This completes the quest, Pride Before a Fall.