As with every boss in Bloodborne, how quickly you beat a boss depends partly on luck, due to the randomness of certain moves. In this case, the RNG wildcard is the pounce attack. He telegraphs it with a roar, but like you say, it happens quickly.
Here's how I beat him. Took at least four or five tries, but I found this strategy to be relatively safe. It'll be a long battle, but it works. And I'd recommend standing away from his legs. He always turns to face you, so if you're at his feet, you'll have virtually no time to avoid the inevitable pounce attack.