Normally, when something as styled as this is being shown to an Android developer. There are only two things that passed through their mind.
"This isn't native behaviour!" "I'm telling you, this is going to take up a lot of time. Why not just stick with the plain old dropdown menu provided by Android?"
Trust me, I also have the same thoughts in my mind as well. Whenever there's styling in Android, it can be messy affair. Fear not! I'm going to show you the ropes on achieving your own stylised dropdown menu with ListPopupWindow and ArrayAdapter.