Tyra is not CC-immune during her Ulti. If you run Agony, you can stun Tyra whenever she Ults, and this will use up most of her Ult, saving your team from a lot of damage.
When Terminus uses his Ulti, use your Shadow Travel. You will be immune to damage and can stay on point/payload while the rest of your team finds cover.
Lex deals a ton of damage, super fast. Make sure you have a loadout where the cast time for Shadow Travel is reduced, because he can easily kill you while you're still casting.
Makoas LOVE to flank healers, and he can deal a lot of damage to you. Your best bet is to use Agony, and stun him whenever he comes after you. This will give you a good chance to run away or ask for help from your teammates.
If Inara begins flanking you, the Agony Stuns work wonders for escaping. You cannot Shadow Walk in TG Warder's Field, so simply Stun Inara and you'll have time to walk out of the field, and then you can Shadow Walk to escape.