Quest objectives
Reach the required (5) Vitality skill level
How to complete the quest?
Vitality is increased when the character takes damage. You can find a secluded place with barbed wire and receive damage from it, healing along the way.
Do not forget that due to fatigue, there may be a penalty for skill leveling. So, try to get some Vitality points in the raid and start a new one (if you focus solely on increasing vitality).