This is the first real "boss battle" of the game and comes within the first 15-20 minutes.
You'll start off on the dragon's back and have to climb up to its head avoiding the electricity from time to time (two prongs will pop out and have electricity between then). Once you get there, attack him a few times when prompted by pressing
After enough damage you will see a cut scene and move onto the next phase. You will have wind blowing you backwards and you will need to progress to the right until you get to the head and can attack again. Just keep moving to the right, slashing the turrets and jumping over electricity until you get there.
The third phase will have a cut scene and move you backwards with wind again. This time, move to the right but jump over and go under missiles as they come at you. You'll get close to the head and be blown back to the beginning before you can attack. Simply move towards the right again and avoid the missiles that shoot up and lock onto you. You have some platforms you'll have to cross and hop back onto the dragons back as you go (and continue to dodge missiles as well) until you've done enough damage to finish him off. You'll see a cut scene and the achievement should pop on the start of the next area.