It's been 11 months now since we brought home a second cat. They have learned to tolerate each other but that's about it. We have hopes that some day they will get along.

Definitely have at least 2 litter boxes.
Close the bedroom door during the day.
The entire family needs to decide who is the "alpha" cat. (Probably the first kitty). Then, you need to greet, play, pet, feed the alpha cat first.

That's what finally stopped the terrorizing in our house. I was treating one cat as the alpha and my husband was treating the other one as #1. The kitties were confused and fought for our attention. Once we both decided that Cammie was #1 Halo's attacks on Cammie stopped.

Good luck.