Tenacity is the quality or state of firmly holding onto something, usually one's duties or personal beliefs.
Tenacity leves are, for the most part, similar to Valor leves in that the only requirement is to defeat a quantity of mobs. However, when the final mob hits low HP, it will run off for reinforcements. Damage over time attacks or ranged attacks can finish it off, ending the leve. Otherwise, additional targets will spawn at its destination that must also be slain.