Everytime you complete a task for Grizzly Adams, and the creature has a boss, you get the right to kill that boss once.
If you ask another task for the same creature without had killed the boss, your quest log will be updated and you lose the right to kill it. But, if your new task requires to kill another creature you keep the right to kill the first boss. Keep in mind you can hold 3 different tasks at the same time.
This dynamic changes after you reach the top rank of Paw and Fur Society's with 100 task points. Now, everytime you delivery a task for a creature, you earn 1 boss point.
There is no limit to accumulate boss points and you can redeem the right to kill any boss of you level range exchanging 1 boss point. The boss points will be deduced from you only if you already killed that boss before, because when you have the top rank, Grizzly Adams gives you the right to kill any new boss for free.