Attack in very deliberate waves. Look for an opportune time and place where the tiny spiders thin out, run right at Rom and hack away at its body 3-4 times and then roll away. The attack where meteors come from the ground has a pretty obvious animation so just get out of its AoE.
A lot of people reportedly have trouble with the meteors that come from the sky but I've pretty much never gotten hit by them. May be dumb luck (Including the Chalice Rom I beat it twice solo, and multiple times co-op with other players) but as long as I'm not letting off the run button, they always hit right behind me. I noticed that when I'm RIGHT next to ROM, the meteors also miss/don't hurt me. Rom's been the most benign boss in the game for me. It's the small dive bombing spiders that you really have to mind, which is remedied by never staying in one place for more than a few seconds.