Far Cry 3 Blood Dragon

Simply kill a dragon. You should get this fairly early, especially if you bring a dragon in a garrison you try to liberate. There are sometimes turrets in the garrisons or nearby, and they can kill a dragon in a few seconds. Otherwise, I found best using the sniper rifle with the explosive ammo. Explosives (grenades, C400...) can help as well. Still, it takes a serious deal of damage to take down a dragon so make sure you don't run low on ammo or health before attacking one.

Try to always stay near a cover, in case the dragon prepares to shoot a laser beam. This can be deadly.

If you're like me and like to unlock the achievements as early as possible in the game, then you can be done with this one when clearing the very first garrison.

Your AI will tell you that there are many alternative courses of action. After picking up the bow (if happens that you die and restart, you spawn in the outside of this room with the bow), go outside and run across in the outside in front of the garrisontowards the other small building to disable its force field. There will be a couple of C4 explosives there on the outside, so you have to throw one of them and blow the shiny thing that's also outside. That will disable the force field and the Blood Dragon nearby should automatically go inside of the garrison and start attacking the enemies. If the dragon doesn't go immediately then you can throw a heart (assuming that you have one) pressing towards the garrison to guide it there.

The blood dragon will most likely kill almost everyone (except the sniper, who is unreachable to it, in an upper position). That fight between the dragon and the enemies must have taken its health at least a bit down. Now it's up to you to do the rest. The weapon that does the most damage against it is the C4, but you only have a couple of them. So, throw it close to the dragon and blow it when it is on top of it.

Sometimes after killing the last enemy of a garrison a cutscene shows that it was freed/taken by your forces. That also tends to calm down the dragon's anger meter and put it outside the garrison and the forcefield back up. That way the dragon cannot enter, so you could stand on the inside and finish the job from there, safer. Just be careful and move to any side when the dragon threatens to shoot its red laser to dodge it.

ALTERNATIVE WAY: Later in the game it's going to become easier to kill dragons, so you can earn this and your Kill 25 dragons achievement a lot faster. When the game finally lets you to freely explore and no longer fails you for deviating from the given objective, you'll often find enemies on the roads. They will come in cars with a mounted weapon on top. If you can get them to leave the car or if you can kill them without destroying the car, and then hijack it, these mounted weapons as well as the turrets that you find in some of the garrisons make a lot of damage to the dragons.

If you can't find any dragon nearby, remember that they'll show up each time you take a garrison's force field down.

Ryowebo has a good strategy with the turret in the garrison. Another way to do it that I found very easy is to plant mines down in a straight line when you find a Blood Dragon. Then you crouch and walk close to it and throw c4 at it, and run in the direction of the mines. When you're a safe distance away detonate the c4. After the Blood Dragon trips the mines, just dance around the Blood Dragon and whatever cover you decide to use. Using c4 and the shotgun. I dropped a Dragon in no time.

Hey guys.

I found another easy way to get this one.
It's during the mission What is this shit!?

Wait until the end after destroying the eggs and jump on the back of the jeep and shoot the dragon while on it,

Here is a Video of if below.