DARK SOULS II: Scholar of the First Sin

The Last Giant is the intended first boss of the game. He is located in the Forest of Fallen Giants, which is accessed by Majula.

From the Cardinal Tower bonfire go down the ladder, if you have opened the gate on your right then go through it and on your left is the elevator that takes you to the Last Giant. Otherwise, go through the area until you reach this point.

The Last Giant has relatively low health and simple attacks. Attack his left or right leg until he lifts it, then quickly roll to the other leg and repeat. Be careful not to run out of stamina, if you are low then roll out of the way and refrain from attacking until you have recovered.

At half health he will rip off his arm, this gives him extended range and higher damage. However, if you keep to the leg tactic then it will not matter. Sometimes he jumps backwards, if he does this then run between his legs and then choose one to hit, he will likely be performing an attack with his arm, so you have an extra hit before he lifts his leg, but don't get greedy.

Once he dies your achievement should pop.

The Last Giant is the first boss (or at least the intended first boss) you will face in Dark Souls II: Scholar of the First Sin. He is found in the Forest of Fallen Giants, which can be accessed through the game's hub area, Majula.
To get to him climb sown the ladder beside the Cardinal Tower bonfire and dispatch the enemies down here. One of the enemies has a sword, and the other has a halberd. Kill them. Facing the ladder, head to your left, and then turn left again at the bridge. There is an enemy in this room who is faking sleep, so don't let him fool you and attack him.
Head through the white fog gate and begin walking up the branch. You will find yourself on top of a bridge with several enemies wanting to attack you, including a deadly enemy with a turtle-like shell that can cause devastating damage. Also, there are barrels full of gunpowder and an enemy above you throwing firebombs which can cause a massive explosion if these barrels are hit, so watch out for him! Dispatch these enemies one by one. Now, there is a very handy shortcut back to the bonfire that can be opened here. There are several explosive barrels stacked up against a wall at the far-end of the bridge, throw a firebomb at these, or get the firebomb throwing enemy above you to do it for you (being careful not to get caught in the flames yourself!). This shortcut leads you right back to the Cardinal Tower bonfire, making it much easier to get back to this point if you die. Rest at the bonfire and get ready for a long journey.
Now, from the bonfire head back onto the bridge, but this time, as soon as you walk out onto the bridge, turn left. This small platform has two enemies on it, so kill them and head down the ladder at the northwest end of the platform. Head down the stairs and turn left, NOT RIGHT. The hole in the wall to the right leads to a devastating area with several enemies and multiple turrets. Furthermore, don't go straight, as you will be locked into that area until you die (at this point you won't be able to get through it easily, so wait until later).
So, after you turn left, you will arrive at a small area with two firebomb throwing enemies above you, sFeveral exploding barrels, and two enemies on the ground. The easiest thing to do is try to lure the firebombs to blow up the entire area so you don't have to kill anyone.
After the area is cleared, head throw the door at the northwest end of the area (from the entrance).
This area is filled with enemies, including another heavily armored enemy. Dispatch them and head to the white fog gate at the very south-middle of the area. Head straight and to the left and unlock the locked door. You're now standing beside the ladder that leads back up to Cardinal Tower's bonfire. Go up and rest, then head back down and through the door you just unlocked. There is a platform in the center of the area with a button on it. Stand on it and let the elevator take you down to the bottom floor of the area. Head through the long hallway (be wary that there is an enemy in the middle of the hallway. Kill him and go forward). Head through the white fog gate and prepare yourself for the Last Giant.

Boss Strategy:

For Melee Users:
This is a fairly straightforward boss, but can be deadly for beginners to the series. When you first walk in, he will be at the far end of the arena and will begin towards you. Run underneath him and begin to chip away at one of his legs. A shield will do you no good hear, so two hand your weapon. Be careful, as he will at some point stomp at you. When he does this, run to the other leg and continue hitting him.
Midway through the fight he will rip off one of his arms and use it to club you. This doesn't affect the boss battle's strategy, however. Continue to attack the legs until he's down.

For Magic Users:
This boss, like all bosses for magic users, can be quite tough. You will have to constantly run away from him and fire a spell off every now and then, but you should be safe under the legs, just like melee users. If you run out of spells, use your backup weapon to finish him off.

No matter which strategy you adopt, once he's dead the achievement should appear.
Congratulations! You've bested the Last Giant!