How to Unlock Jill Guide
In order to unlock Jill you'll first need to reach the 6th Trainer Rank (or higher). Once you've accomplished this you'll want to accept an errantry to Torles mountains in the winter time and when you're there pick up the Giant Footprint which is at the far northern end of the area.
Reaching the structure with the Giant Footprint in it isn't an easy task, unless you have high enough intelligence to open up all the secret paths which make getting here easier you'll have to take a route that eats up 100 - 150 Energy. Where this structure is, is basically the opposite end of the area from where you start. I'd describe how to get here but any directions I could give would be confusing, best advice is save before you come here and reset once or twice to learn your way around.
The next time you go to do a Torles Errantry the man there will tell you about a monster that has been seen in the area, then Colt will mention the footprints you found. This next part of the quest to unlock Jill is completely random. First up, you'll need a monster that is strong enough to complete the Torles Errantry.
You'll then want to take that monster on the Errantry and complete it until he encounters Bighand in a battle, like you see in my screen shot above. When you choose this Errantry it doesn't matter what monster you choose to fight or what rank they are - Bighand has a low % chance to spawn in their place instead.
I recommend that you save before the Errantry and keep running it over and over until you encounter Bighand. It just takes too much out of a monsters life to keep running the Errantry in hopes of encountering Bighand one day. Defeating Bighand will reward you with the Big Boots item which you'll want to take to the Lab and use them as secret seasoning to unlock Jill.