Strike a Melee Target with Thrust 5 times, use Shield-Breaker on 2 vulnerable Ranged Targets, use Charge on 2 vulnerable Charge Targets, and then return to Galathia Brightdawn at the Argent Tournament Grounds.
If you lose your lance, you can get another from any of the Lance Racks near the stables or the Sunreaver Pavilion.
Most of the tournament's competitions require competitors to master the command of a mount in battle. In order to familiarize you with mounted combat, we've put up training dummies all over the northern part of the tournament grounds.
Visit the stables outside the pavilion, equip your lance, and mount up on the Sunreaver hawkstrider. Familiarize yourself with the mount and use its abilities to defeat the three different kinds of training dummies.
Well done, <name>. Mounted combat is often hard to pick up for those accustomed to fighting on foot. I have no doubt that you'll continue to improve with practice, which is more than I can say for some warriors.