Okay, where you get the quests from Mr Qi, on the right side of the room next to the display where you can purchase things with your Qi gems there is a little statue with a blinking light display belly. Click on that. That'll tell you all the things you need to do. It's not the Qi quests, though you do have to do some and buy all the recipes that you need to purchase with Qi gems. There's a LOT to do, honestly.
You have to ship all the things, buy all the obelisks and the golden clock, slay all the monsters, max all the friends, max all your skills, find all the stardrops, cook all the foods, craft all the stuff, catch all the fish and find all the walnuts.
Hold up, I just came back to this and noticed something I hadn't before...
You got a picture.
Was it perhaps called a War Memento? If so... who do you know in town that has been to war? That person will give you something in exchange for the war memento, and you'll have to figure out who would want that thing... and when you give it to that person, they will give you yet another thing. This will keep going on until you receive from someone something to give to the woman that gave you the war memento picture to begin with.
You can get the full answer on what is received and who you should give each item to on the wiki. You can read that here: >LINK<