Finally started on Bloodborne a few days ago, and finished off Cleric Beast in two tries (Gascoigne was closer to 8-10) and yeah, the trick to Cleric Beast is not locking on; he's too big, and the arena's too small (although do lock on if you toss a molotov at him, then immediately un-lock). Other than that, it's just the standard Souls game tactic of "circle strafe, and stab in the ass."
And remember, you're under no obligation to actually kill the enemies on the way to the boss. Just take the unlocked shortcut to the bridge, sprint past the crows and the brick fucker, and you're invincible when passing through the fog door.