You are having problems because the geometry is a mess. You don't want any of those elongated triangles.
I would try it like this:
- DELETE all top faces.
- See which of the vertical edges can be dissolved without losing detail. - Goal is to have relatively even spacing.
- Select the outer edge (green/sharp in your picture) and inset it far enough to have room for the desired bevel. Be careful not to overlap any geometry. In that case you'll need to cleanup manually after insetting.
Alternatively to insetting you could also extrude the edge by scaling inwards and possibly smooth out the resulting edge to avoid overlaps.
- Try Grid Fill or manually fill in the rest of the top faces.
After step 3 you could already try to bevel it and see if it gives you a better result.
I hope this helps a bit.