When you talk to Addie Fizzlebog, she will start following you. She has an experience bar over her head that will fill up as you level her.
You have to level her through the three stages:
- Apprentice Training
- Journeyman Training
- Expert Training
in order to complete the quest. The stages auto-complete, so you only have to turn in the quest at the end, when she has finished the Expert stage.
There seem to be two ways for her to gain experience while she is following you:
Resetting the Poorly Set Traps in the area by interacting with them.
Killing any of the beasts in the area like Skittish Does, Pinerock Elderhorn, Pinerock Stalkers, or Bristlefur Bears.
When you pick up the quests:
- Moose Shootin'
- Lion Stalkin'
- Bear Huntin'
from Hemet Nesingwary at the same time as this quest, you should be able to get her to Expert (or close to) just by completing these kill quests.