The Cathedral of Blue area of Dark Souls 2 is a comparatively small part of the game, but as well as housing the Blue Sentinels covenant, it also contains a pretty meaty boss fight. You'll find the Cathedral of Blue adjacent to Heide's Tower of Flame, and you'll be taking on the Old Dragonslayer boss the minute you step inside. Here's how to finish the fight, and gain access to Targray, leader of the Blue Sentinels.
How to kill Old Dragonslayer
There's one big weakness that melee characters can really exploit in this fight, and that's the left section of the boss's body that's exposed whenever he attacks. Have your shield at the ready, simply circle around the boss in order to avoid his lunging attacks, and leave yourself free to dart in and dish out your own damage. Just make sure you get away from the boss whenever purple mist appears around him, as you'll struggle to block the incoming magical damage. You'll also need to evade the arcane missiles he fires from time to time.
It's extremely difficult to fight the Dragonslayer from range, as he moves far too quickly for you to maintain a suitable distance. If you play as a ranged class, you should instead follow the melee strategy outlined above, and simply fire off your spells and arrows from a close-up position.