Esty's ending requires the following:
- Attend the first lake event (Esty does not go to this)
- Do all of Esty's Upgrade requests. For reference, the last one is for a Gorgeous Dress.
- Finish with a town popularity of 90% or more
There are several events through the game where you talk to Esty regarding her search for a boyfriend. I believe these are tied to town popularity levels (which maps to Esty's FLV). These will mostly show up as you play.
Esty's ending is independent of the True/Good/Normal endings, and will be available as its own selection like the Pie/Millionaire/etc endings.