This boss uses a spear and lunge attacks that can quickly close the distance even if you try to stay away from him. One good strategy is to keep close and keep circling around him, evading and counterattacking when he swings his spear. He also has a projectile attack and an AoE (area-of-effect) attack which you should avoid by staying away.
Timing your evasion can be tricky since the boss is fast as well. However, as long as you learn his stance, you'll be able to anticipate the following attack and how to react to it. Running out of stamina to evade is always bad news so don't get cocky and hit more than 3 times in a row, unless your stamina can accommodate it.
Defeating the Dragonslayer will give you 20,000 souls, Old Dragonslayer Soul and Old Leo Ring. Go through the next door and you'll find two chests. Loot them for Cracked Blue Orb x3 and Heide Knight Iron Mask and Tower Shield in the next chest.