Make your basket almost/completely full, then leave Alanya for a day (with Mimi) and you'll get a scene upon returning. Several of the following events are almost automatic if you keep Mimi in your party. (10 friendship)
15 days later, go to Atelier Totori. Mimi forces Totori to help around the house more... XD (15 friendship)
15 days later, return to Atelier Totori. Mimi helps Ceci. (20 friendship)
15 days later, return to Alanya again. Mimi is still jelly and refuses to talk about her family. (25 friendship)
15 days later, you guessed it, go to Atelier Totori. Mimi has no friends. (30 friendship)
After you get Iron rank, talk to Cory. Cory knows what's going on just a little too well. (35 friendship)
Talk to Mimi. Supposedly this also occurs if she's in your party and you go somewhere with her. Optional.
Do 25 requests for Filly, then talk to her. (45 friendship)
After Year 2, 6/1, and 15 days later, go to the Adventurer's Guild. (50 friendship)
At least one day following that (I tested; it doesn't work the same day!), get a rank up.
3 days later, synth at Atelier Rorona.
15 days later, talk to Cory to watch Mimi rank up. She's back in the party.
Go somewhere with Mimi while you're building the boat. (60 friendship)
When the boat is finished, put Mimi in your party and take off. Then beat Flauschtraut with Mimi in your party.
An event will occur after you leave the Frontier Village. You'll get the ''Aristocratic Love'' trophy.
Defeat Evil Face by Frontier Village. Mimi doesn't need to be in the party.
Talk to Mimi about being the world's greatest adventurer (it's a short, surprisingly important scene). Then level her and Totori up to 50 for a scene. If it doesn't trigger, level up another person.
If you want to get all ends, don't get Mimi up to 50. Leave her hanging at 49.