Neverwinter

Update: Old method works again! Below is the original group method. It can be done solo with very good results (quote courtesy of FrogTheWarrior, with information corroborated by Jappe XBA):

"Gosh, I killed one dragon and it took FOREVER - I'll never get this achievement!"
First and foremost, this achievement is going to take a long while. It's not short. Luckily, it's also not as long as you fear, either. All told, it should take 15-20 hours of boosting to secure this achievement depending on the quality of your gear. You kill 50-100 dragons per hour.

Here's how it works:
1. Get a group of 5 people. Making a session is ideal. You want a Cleric in the group (if less than 10k gearscore), but a Guardian is totally worthless.

2. Go to normal Caverns of Karrundax. Level 60's can queue for this, but be careful. If someone leaves for any reason, you can't reinvite them - a random player will join instead. He probably doesn't want to grind dragons.

3. Fight all the way to the end. This takes about 15-20 minutes.

4. Now we're at the good part. You want to start the fight with Karrundax and kill the two Dragonlings. Once they're dead, you need to die. All players should stand in fire and kill themselves ASAP. The fight resets.

5. Rinse and repeat 500 times.

Solo?
Yup, this is possible even with mediocre gear at 70.

The Details
Once you get to the fight, killing the Dragonlings should take anywhere between 1-2 minutes. It starts to take longer as you'll get more and more injuries. You can mitigate this a little bit by buying Divine Wound Kits (earned during some weekend events) off the Auction House. Clerics shouldn't bother with these. The injuries have the following effects:

Legs: The dragons melt the steel off your boots; trudging through molten steel makes you slow.
Torso: You lose a substantial amount of HP. Your healer will no longer be bored.
Arms: Remember those sick crits you got at level 30? Well now you get to see those numbers again instead of the level 60 ones.
Head: Your ability cooldowns now last ten minutes instead of ten seconds. That's sarcasm.

You can buy wound kits to deal with this, but it will take 100 gold to buy enough to clear every injury you'll ever get. Most likely, you're too poor and you're stuck fighting with foam swords.

In the end, this method isn't that bad. My initial solution said to commit suicide using the "I Am Stuck" function to kill yourself. Rumor says the devs get a ping every time you do this so they can investigate. Do not do this. Another solution says the developers will not care. Maybe not, but none of us know anything at all. I don't recommend it and you do it at your own risk. Once you learn how to die, it's only marginally faster and you'll still need the same number of sessions. My group had everyone try to die and if they didn't die to the fireballs, then you use "I Am Stuck" to kill yourself to limit the time wasted.

So if you want to take the risk like I did, once you kill the dragons you press and scroll all the way to the right. Select "I Am Stuck". This will give you the option to kill yourself instantly and respawn at the nearest fire.

Good luck!

UPDATE:
With the Maze Engine update this solution is not valid anymore. The skirmish is can't be accessed anymore.


The Pirate's sky hold skirmish has a dragon to beat at the end.

With a lvl.70 you can solo this skirmish quite easily. I'm a healer and have no troubles. Takes about 5-10min. Just head to pirate's sky hold and talk to the guy with the skirmish icon above his head.

If you're lvl. 40-47 you can queue this skirmish.

Between the waiting times in the well of dragon, you can visit pirate's sky hold and kill this additional dragon. It even gets you some astral diamonds