Shell Shield has the longest base cooldown time of any shielding ability and Makoa lacks a Legendary card that reduces its cooldown. Shoot down the shield when possible to ensure its usefulness is limited.
Dragon Punch will inflict no damage to you as long as you stand in your Assert Dominance field. Be sure to hit the ground and plant your flag before you get punched though, or you'll die in midair.
Unless the enemy Barik is using the Fortify Legendary card, his Barricade only has 5000 Health. It can sometimes be more advantageous to simply destroy the Barricade instead of sidestepping it.
The easiest way to play bk is to sit in the back-line and throw bombs. If you want a challenge try using the poppy bomb to launch you across to the other side of the enemy and wreck! Don't stand in one spot always be moving!
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.