As you cross the Great Bridge, a huge creature will leap down and challenge you. This is the Cleric Beast.
As long as you don't get greedy, Bloodborne's first boss isn’t too difficult. Start with the tried-and-true 'dodge left and circle the boss' method. After a few strikes, the Cleric Beast will be open to attack. Use this moment to deal a bit of damage, but be sure to pull away before he swings his arms back. This tactic will also help you avoid getting snatched up by the Beast's hand-crushing attack.
The circling strategy will steer you through pretty much the entire fight, but the Beast has a few more tricks up its sleeve. When it punches the ground immediately in front of him, stay back and wait until the punches subside. Finally, watch out for his three-hit combo - it will likely kill you if the whole thing connects. As long as you sidestep and keep your distance during this time, you'll be OK.