This achievement asks you to complete the game on the hardest difficulty of them all for Conan. That difficulty is called King difficulty.
In order to unlock this difficulty, you must first complete the game on the second to last difficulty, Hard mode. Once you accomplished this, the difficulty is available to play through at anytime.
From start to finish, your best friends will be three of the cheats that unlock if you complete it on Hard instead of Normal. Make sure those Cheats are on before you attempt to go through all twelve acts. Once you earn magic, constantly abuse it in enemies. For example, with the lions, use the Stone Armor magic. If you are surrounded by a multitude of guards, use Rain Of Fire, as it will eventually kill them all. If some of them are away from it and don't get killed, make sure you go near them and try again until they die.
As for boss tips, I don't know if it was intentional or just a glitch, but I used Void to avoid Graven's honing attack, since it has invincible frames. He was somehow stuck in the Void magic, so I was able to constantly assault him without losing any energy. In other words, he never moved while Void was turned on, so I drained his lifebar pretty quickly. None of his tactics or strategies he uses, along with the other bosses, changes. The only difference here is that all enemies are a lot of tougher and can hit for a lot more damage.
Make sure you constantly block, attack with two-handed weapons in each hand (which is what I did throughout the entire game) and use magic all the time. By going through the game, you should be able to complete King difficulty in no time. I was able to complete it in less than 4 hours time!
Have fun and good luck!