I'm not sure what the OP's tanking experience is. If you're like me and have very little experience take the above suggestions and one more thing...
Teach yourself how to properly maneuver the mobs as well. I'm always forcibly reminding myself to turn the mobs away from Vette. Her hit percentage will go way up with their backs turned to her which in turn means she'll hit them more often, which in turn will burn them down faster.
Get yourself used to doing that in open world so it's second nature in FP's and OPS.
I'm only a lvl 19, but looking at the immortal skill tree as i'm leveling, it looks like our survivability just skyrockets as get further up the tree. Our cc isn't the greatest compared to others, but between dmg mitigation, accuracy reduction, defensive procs and damage absorbtion skills it really just looks like you have to get a handle on your abundance of talents and stay geared appropriate to your level.
Sorry, got off on a bit of tangent there.
TL;DR - don't lose heart, complete side q's / bonus objectives, gear up, it's fun as hell.