Inara's ultimate has a long windup time so before using it make sure to be in a safe spot with enough health to survive bombardmemt. It has an obvious voice line letting the enemies know to focus you so using damage reduction first can help.
If the enemy Inara is using the Tremors legendary then focusing on destroying her walls when she creates them will significantly decrease its effectiveness. Use the anti deployables item and not anti shield since she deploys a wall not a shield.
Inara's CC immunity skill can help her nullify effects such as Tyra's aoe fire, Willo's Dead Zone and Jenos' Void Grip. It can be used during the effect as an immediate cleanse.
Inara's Impasse has very high health and can be annoying to take down, especially without Bulldozer. If the enemy Inara happens to use it near the payload, remember that if the payload touches it it will instantly be destroyed.