reflection surface - not flipped sprite (shader?)

[s4m_ur4i]

I searched around but didn't found something. But maybe someone else has already thought about and found something:

I've got a 2D Sprite and would like to add reflection to this sprite. Since this can take have on performance let's consider a scenario:
We got a glass pillar (2D Sprite) and it should reflect only a player (2D Sprite2).

I am not talking about something you see in different games like "water reflection" were you simply flip a sprite and render it beneath.
What I do is searching a way to apply this to different sprites of any kind.

 like: in a glass world. And no I do not want to you tree.js or babylon, which are capable of this. Since I only use 2D environment stuff it would be way too much for only reflections.
This reflections need not to be "real", it's more a faked way of doing it I think but I have not found a simple way of doing it.

The perspective is top-down like a gameboy zelda game and you have 8 directions (up, down, right, left, down-left, down-right, up-right, up-left).
So the direction of the player Sprite also changes a lot.

So any kind of suggestions and hints would be appreciated