"A Single Deadly Bite" is a challenge from Tiny Tina's Assault on Dragon Keep DLC
You must defeat her without her managing to regenerating health. This is most easily done by avoiding her corrosive-nova attack. It is telegraphed by her gathering Green Healing nodes around her. When you see it, run away. The second best option is just blast away quickly with your most powerful weapons and keep moving away. Putting cover between the Vault Hunter and her is no assurance of being able to avoid the attack.
Ranks and Rewards
Lv 1 - Defeat the Spider Queen without her healing