Road to your objective
The first colossus is found not far south from your starting position. Equip your sword and hold (R1) to find your target. You need to stand in a sunny location (blue flames).
Use your horse to reach your objective. You can mount the horse by pressing Triangle or by jumping onto him. Press Triangle again to dash. You'll encounter the first fruit tree (see "Increasing Your Health") - use the opportunity to pick-up the fruit.
You'll need to climb to the location. Climb onto the green plants by pressing R2. Continue forward (you can move faster by charging your jump button (X). Hold the jump button while nearby the upper ledge to climb onto the platform. Continue climbing until you've reached your objective - a short cut-scene will begin during which you encounter the colossus.
The encounter shouldn't pose much difficulty. Equip your sword and jump on his left leg and hold onto it by pressing (R2).
You'll encounter a blue crack on the boss's leg. Attack it by pressing Square and press it again when the strike is fully charged (look at the yellow strength gauge in the lower right corner - the dots will widen and touch the edges of the gauge's area - your attack will be the most powerful that way). You can release the strike earlier, but it will be weaker. Sometimes, such short strikes are necessary in order for them to land before the enemy manages to throw you off him.
Every vital point has a limited amount of damage it can take. In case of cracks, you need to look at the boss' health bar (upper left corner) - if your attacks do not cause any damage, you need to switch to a different area. The two glowing marks (another type of a weak point) found in the upper part of the boss will stop being lit after they take a certain amount of damage. In this case, a cut-scene will begin once you've dealt a certain amount of damage to the boss.
When the colossus has fallen, grab one of the upper parts of this back and climb to its head. Remember to release your hold while in a horizontal position in order to regenerate your strength.
The next weak point is found on top of the boss' head. Charge the first attack then follow with faster strikes - the colossus will attempt to shake you off its head which will interrupt your charged attacks. This is the most difficult point - the opponent will shake his head violently, which will take a lot of your strength. If your strength falls down to zero, the hero will let go and receive falling damage making you an easy target for the boss. Moreover, you'll be forced to repeat the climb starting from the colossus' leg.
After you cause your opponent enough damage (indicator point stops being lit) you need to descend and jump to the boss' right hand (his elbow), which holds the colossus' final weak point. If you've dealt enough damage at the earlier spots, a few hits should be enough to defeat the colossus. If his health goes down to zero, a cut-scene will play out depicting your victory. As always, you'll be taken to the castle in the middle of the map, where you'll embark on the search for a new target.