hm... Just a strange idea: Why it is always a Monster with set Lifepoints you have to bring down?
Why not doing the opposite?

Lets say you can rise the Lifepoints with attacking the Monster and you can not kill it so fast...
When no one is attacking it the Life will fall again and once at Zero everyone gets the reward...
To avoid abusing you have to do a set ammount of damage for your quest, so it will not go down too early...
That way most players have the chance to reach the spot where the monster spawned and can do their quest...
Maybe you can add some mechanics to trigger when the Monster have too much life, example: something will happen on next spawn or Healing nearby Monsters or anything we do not think of yet...