What’s the strategy to beat the first boss seen when you’re escaping your jail cell in the first part of the game? I haven’t had any luck.

There's a little side door to find, you have enough time to sprint through it before the boss gets angry.

The first time you see the Asylum Demon it's pretty much impossible to beat him (as I'm sure you've discovered). There might be a way to escape though...

@captain_max707: what is the way to escape? Have you gotten past him?

Just keep looking. Often Dark Souls hides things around the periphery.

Thanks guys.

Folks have already given you your answer, I just wanted to point out that there's a secret weapon you can obtain if you beat the boss without actually going through said door and receiving your equipment. It's a neat, little thing.