Bloodstarved beast is a hard boss, one of the hardest if you do not know what you are doing. This boss is also optional, like Cleric Beast and later leads you to the Yar'gul, The Unseen Village. The best way to approach this is to have your antidotes ready, and stocked on bullets.
Bloodstarved beast's move are pretty radical, and luckily they are pretty predictable in the second and third phases, much like Father Gascoigne. Use your gun to stagger, then use your visceral attack, if your in a dire situation, use Blood cocktails, use an oil pot, then toss some Molotovs.
If you have questions, comments or feedback, let me know.
Note: The best weapons I found to be useful are long ranged weapons.