Among the Champions

This macro trivializes the fights:

/run GossipFrame_GetTitleButton(1):Click()
/leavevehicle
/cast Howling Blast [REPLACE WITH ANY RANGED ABILITY]

Bind it to some key on an extra action bar, then when you have to do the stupid vehicle quest on the horses, talk to the NPC and spam it. It will select the first dialog option, immediately dismount you and oneshot your opponent with a ranged spell during the few seconds where it's still vulnerable. Saves 5 minutes of running around, putting shields up and charging every day.

EDIT: Fixed macro for Shadowlands

Update to seirl's macro for Shadowlands:
/run GossipFrame_GetTitleButton(1):Click()
/leavevehicle
/cast Conflagrate

Replace Conflagrate with whatever instant-cast instant-damage ability you have. Put it on a secondary action bar, talk to a champion and spam the macro. Works every time.

If you have any problems with this quest, you can try following strategy. If you do everything correctly, your mount shouldn't lose more than 5-10% hp.

1. 
   
2. Fully stack Defend before the fight begins [default binding: 4]
3. 
   
4. Start the fight by talking to NPC
5. 
   
6. Use Shield-Breaker twice [default biding: 2]
7. 
   
8. Use Charge [default binding: 3]
9. 
   
10. Use Thrust everytime it's ready [default binding: 1]
11. 
    
12. Use Defend everytime it's ready (well, maybe not everytime, but make sure you have 3x Defend)
13. 
    
14. When enemy gets one layer of Defend, strafe away and use Charge
15. 
    
16. Repeat steps 5-7
17. 
    

When you talk to the NPC, try to stand behind and strafe little bit away from the ring when the combat starts, this should give you enough range for first Shield-Breaker. You have to keep range until you completly remove opponent's Defend, after that, you want to stay in his melee range so he cannot use Charge nor Shield-Breaker.

Keep in mind, that Thrust does NOT trigger GCD, so you can use it with Defend at the same time.