Although Belfry Luna is an optional area of Dark Souls 2, completing it does serve a benefit for another area in the game, Sinner's Rise. By completing Belfry Luna, you'll obtain the Bastille Key, which will be a great help when you take on the Sinner's Rise boss.
In order to gain access to Belfry Luna, you'll need a Pharros' Lockstone. From the Servant's Quarters bonfire, head down the ladder, kill the dog and insert the Lockstone into the hole in the wall to reveal a secret door. Attack the door to reveal the path to Belfry Luna.
Once inside, speak to the bellkeeper sat by the door. He will give you the chance to join his covenant. Head up the first flight of stairs and kill the first dark bellkeeper. These guys can cause serious damage, and will still hurt you even with your shield up. Thankfully, their attacks are easy to dodge, so just step back and then counter. There are a bunch of holes in the floor, fall through the one with the curtain hanging through it to in the secret room on the floor below to get a bunch of items.
Head back up to the second floor and kill two more bellkeepers. Don't step too far away from them, as they'll throw firebombs at you and are laser-accurate.
In order to open the gate to the mist, you need to head up the ladder and ring the bell. There are a bunch of bellkeepers here, so take your time in dealing with them. Try not to run around too much and alert all of them at once, as they can be a real handful. There's also a chest containing a Radiant Lifegem and Twilight Herb here. Pull the lever to ring the bell. You can now get to the boss, the Belfry Gargoyles.
How to beat the Belfry Gargoyles
The Belfry Gargoyles are an homage to one of the earlier bosses in Dark Souls, but are made much tougher as the game throws many more of them at you with little rhyme or reason. Before taking on the boss, stock up on Lifegems and Green Blossoms.
The Gargoyles are incredibly tough, and attack in force. You have to deal with up to five at any one time, and they use the Streets of Rage-style tactic of trying to be both in front and behind you, making it impossible to block attacks.
That's why your best bet is to constantly run around the perimeter of the roof, sprint-stabbing when you get the opportunity. As you're running around the edge of the map, the gargoyles tend to bunch together, so your running slice will likely hit more than one of them. If you're a mage, run away, cast and move again once they get close. Only attack once then run again, as they attack quickly and you don't have time to get your shield up. Rolling is also a good strategy. Keep plugging away and one by one the gargoyles will die.
After they're all dead, proceed through the door, down the spiral stairs and grab the Southern Ritual Band from the chest. Walk along the bridge and ignite the bonfire. You can head down the ladder next to the bonfire to kill the dogs, you'll be invaded by the Dark Spirit Vorgel the Sinner, a shield and spear wielding enemy. If you have a shield with full damage reduction, his stabs bounce off and he's easy to deal with, providing you roll away from his lethal combos. At the top of the stairs in this area is an Enchanted Falchion. The Bastille Key, which you'll use in Sinner's Rise, is under the archway.