This Achievement is for killing the first boss in the game, the last giant. He can be located in the Forest of Fallen Giants. Upon reaching the second bonfire, you should see a ladder off to the right-hand side of the room. Take that down, being mindful of the knight playing dead near the edge of the bridge in the room. Another knight will be coming across as you enter the area, so quickly take them both out and head into the next room. Another knight will be playing dead here next to the fog door, so take him out and go through the fog.
You should see something that looks like a giant tree branch in front of you now. Go up that and turn around on top of the castle wall. Kill the two enemies in front of you, then make a decision. There's an enemy on top of the wall who tosses firebombs at you, and the lower area holds a bunch of barrels that will explode if one of those lands near them. You can either go to the lower area and run like hell until you drop down to another area, or you can go up the nearby ladder and take out the firebomb guy. If you do choose to go up, keep in mind that the second boss of the game will drop out of the sky to make an early appearance. You don't have to fight him here, though, and I really wouldn't recommend you stick around for it unless you know what you're doing.
Once you've made it past that area, you should be in a place with a long path straight ahead leading to an arch. There's an NPC sitting next to it and an unlit brazier. Go up to him and keep talking until he starts repeating himself. This is Mild-Mannered Pate, and you can summon him to assist in the first boss fight if you go through the area next to him. Go through the arch and a gate will come down behind you. There aren't too many enemies in this zone, but they can quickly overwhelm you, so just take it slowly and try to focus on one of them at a time.
The path here is very straightforward, and will eventually lead to an upper wall of the castle just over where you first entered the area. Drop back down and talk to Pate again. He'll give you the full white soapstone, a very useful and important item for having other players summon you into their games. Once you've heard everything Pate has to say, head back towards the small set of stairs and the ladder that lead you into this area. There should be an arch on your right, stop just inside there.
This next area has more kegs and some enemies up above. Again, they will try to catch you with firebombs for quite a lot of damage. If you have a firebomb of your own, the best option is to toss it at the barrels (making sure to be well out of the range of their explosion), then quickly sprint across and kill the turtle knight on the other side before he has a chance to attack. These guys can do a lot of damage, so you don't want to fight them on equal terms unless absolutely necessary. If you don't have a firebomb, you could try to bait the enemies up above into tossing one down at the kegs while quickly running out of range of the blast. It's risky, but very doable. If you don't feel up for that, you're going to have to run across and fight that turtle knight, which I really wouldn't advise, unless you can attack him from a distance.
However you choose to go about it, you should now be through the arch the turtle knight was guarding. Take a left and there should be two enemy knights in your way. Take them out and go through the fog door. You're now in the area directly behind where you came down the first ladder next to the second bonfire. Go past the unlit brazier and to your left, open the door and go back to the bonfire to recharge. Now come back down and through the open door, then onto the wooden lift on your left. This leads down to a long corridor which leads straight to the boss. Watch out for the enemy hiding in the doorway on your way towards the fog door. So long as you're in human form, you can now use Pate's summon sign to give you a hand with the boss himself (as well as another player, if anyone has one down in the area).
The Last Giant might appear intimidating at first, but he's actually pretty simple to take out. As soon as the fight starts, dash straight ahead and through his legs. Now quickly lock onto him (click RS), then swipe at his ankles once or twice. This is key, do not attempt to simply wail on him with everything you've got. That's a surefire recipe for suicide.
Limiting your number of strikes will also keep you ready to quickly roll or backstep whenever the giant lifts up one of his feet. This means he's about to stomp, which can lead to some pretty heavy damage. He'll either do one stomp or alternate feet for a total of three stomps. You can't dodge these if you're committed to four or five hits in a row, so watch out. The giant will also very rarely flop down on the ground, which can instantly kill you if you're caught underneath. The upside to this is that you can get a ton of free hits in while he's prone.
Keep repeating the pattern of running through legs, locking on, swiping once or twice, then turning off the lock on and running away. About halfway through the fight, the giant will rip off one of his own arms and come at you again. His range and damage will have increased after this point, but the strategy is still the same. Just keep at it and before too long, you will have felled the first boss in Dark Souls II.