Raum has a big hitbox, and Inara's bloom is impressive. So, jumping with her (and away from his gun) allows you to hit him more than he hits you.

Get Nimble from the item shop. Being lighter on your feet and with proper positioning (especially with warder's field enabled), you can circle him counter-clockwise (away from his gun). This allow you to hit him without him ever hitting you.

Raum gets his cardio in and likes to run. Be sure to get the Treacherous Ground talent. That will stop him in his tracks with a quick cripple.

Impasse will soak up a lot of Raum's damage from his ult.