You have to be on an even generation (2, 4, 6 etc). Getting Mimitchi is very straightforward - take perfect care all the time and pause it when you're not there! Take perfect care of the baby and get the best child. Take perfect care of the child and get the best teen. Take perfect care of the teen and get Mimitchi...
It's not that hard because there's nothing "special" that you have to do. Avoid snacks if possible but one here and there won't hurt. Keep it on a minimum weight and exercise regularily, keeping hearts no lower than 3 full. Once all Hungry Hearts are full, DON'T feed it two more meals - it could get sick.