Buddha's Perseverance is an achievement quest. Once you reach a certain level for your character (in this case, Five Dragons 1 or level 60) you will receive this quest.
You are not required to kill any mobs or do any tasks. All that is needed is to go meet with a NPC who is offering a reward for your character's level achievement.
For White Clans, the NPC's name is tavernkeeper Piao Ruoyan (in Jinan). For Black Clans, go find Wang Shierniang (Datong). Look for the white exclamation marker on the ingame map.
Description as follows: Blood Siphon Panacea: Absorb 0.2 of damage inflicted by enemy into Life
Spirit Siphon Panacea: Absorb 0.2 of damage inflicted by enemy into Vital Energy
Your character receives 2 of the selected Siphon Panacea item. To use it, right click on it and the item count in your bag decreases by one. A related icon will appear by the status window in the upper left corner of the screen near where buffs appear.