Among the Champions

Yes. Do not attempt to do this quest while feeling annoyed and impatient. You will end up killing someone irl.

You can complete this quest while in a raid.

Well, like pretty much everything PvE in WoW, once you learn the correct strategy, this becomes a matter of execution rather than strategy: as long as you don't mess up, it's fairly trivial.

The strategy above does work very reliably, but it takes a fair amount of time. You end up spending 70% of the time wailing on somebody with 3-stacked shield and 30% attacking a target with 2. Dailies should be done quickly and efficiently, so a slightly more aggressive strategy works far better, in my opinion. To give you an idea, the last time I did this using my own strategy, I ended my last fight at 25k health. By that, I mean I won all four fights in a row without healing at all between any of them, and I still had 1/2 health left. I finished all four in the time I saw others do one using the above strategy. This same strategy can also be used for an easy solo of the boneguard commander on that daily, since he uses the same attack patterns as valiants and champions.

First, a refresher of the usual strategy, as all of these same rules apply with my method:
1. Open all fights with 3-stacked shield
2. Stay on top of them all of the time (aside from the exceptions below)
3. Never use charge
4. Spam thrust constantly when you're not using shield breaker or refreshing shield
5. When they try to gain range, use shield breaker and again close to melee

However, there's something you can do to greatly speed up the fights. There's a very slight delay between you moving to charge/shield breaker distance and them actually using one of those attacks. If you very quickly strafe out of melee range to use shield breaker, then immediately strafe back into melee, you can almost always launch a shield breaker without taking any kind of retaliatory attack. This can be done fast enough to be done in between thrusts, in fact. At most, probably due to latency, I will be hit with one or two shield breakers using the above method across all four fights, and I simply hit shield again to regain that last stack.

Using the above technique, you can maintain 3-stacked shield at all times, while the champion you're facing will have 0-1 shield stacks instead of 2-3. Fights go far, far faster in this way.