Dark Souls & Other Souls-Likes

Which do you want to kill first? You'll have to kill both first for completion's sake (on NG+) but Ornstein is a lot harder to kill second on NG+.

General battle strategy:

Run around outside of the room, getting them caught on the opposite sides of pillars. WATCH ORNSTEIN AT ALL TIMES! If your shield is good, you can tank both of them (even Smough) pretty easily - though not both at once.

Killing Ornstein first? Fairly easy. Just keep running until he overextends to attack you. Hit him a bit (has long recovery times) but don't invest too much Stamina, and repeat!

Killing Smough first? Harder by a good amount. Can either try to make some distance and force Ornstein into doing his lightning bolts (need to be far but not too far from him) and let Smough rush you => punish him, or repeat a hit&run attack.

Phase 2!

Whoever survives will become a lot stronger(and bigger) and have HP restored to full. They will have more or less the same attack patterns as before, except faster/stronger. Both of them gain this slam attack which will do excruciating damage (if Smough) or good damage (if Ornstein) around a large aoe around them, so back off whenever you see them rise up into the air.

Ornstein gains a new stab attack which is difficult to evade and does very high damage (might oneshot depending on build). Telegraphed by his blade glowing all lightningy.

Smough's weapon is now electrified so tanking him will be painful for you.

Regardless of which it is, you can still use pillars to recover and stuff. It may be advisable to save ranged damage until the second phase as that is when attacking safely becomes very hard. Finally, remember Humanity doubles as a healing item (longer use time than Estus - beware).

Good luck! Many people consider O&S the most difficult boss in the game if done solo.