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Where are you running it from?
Firekeeper bonfire makes it a "straight" run, just ignore the sentinels.
"Solaire" bonfire, you can take a running jump on the spiral staircase on the platform (might have the Titanite demon in a side room? its been a while since I played a full run)
Run by the Silver Knight, up the stairs, turn around and run/jump over the edge. You need to dodge the arrow firing guy and the sentinels by the fog gate, but it is also a quicker way to the boss room without going the long way.Also if you haven't beaten O&S yet, Focus on one only as phase 2 gives the survivor full health again.
(Ornstein first leaves the easier Phase 2 IMO)
Got to ornstein and smough in dark souls remastered - honestly feel like this fight wouldn't be half as hard / frustrating if it wasn't for the length of the boss run! Also just struck by how much easier the bosses in DS1 are vs. Elden Ring. In ER there's more tools to make the fights easier, but on a fundamental level the bosses are much more aggressive and have bigger movesets to predict etc.