Dark Red To Green???

You will need to get all the old red dye out first. Lighter greens are quite tricky, any warmth in the base will go muddy.
So start with colour removers (assuming the current colour is from oxidative dye) then bleach to a light yellow shade.
Directions Apple Green is a similar colour to your swatch.

Just noticed that you say it's MP Vampire Red with no bleach, so you probably won't need a colour remover to get the red out, you just need to fade it there are some tips on how to go about that here:
http://www.hairdyeforum.com/index.php/topic,1704.0.html

As Wicked Pixie says though, after you get rid of the red, you will need to pre-lighten for a light, bright green like that.

Just as an aside, if you really don't want to bleach, I use Directions Alpine Green on a section of my hair which has a natural light brown base at the top and a dyed mid brown on the ends and it comes out quite a nice dark green with more of a blue base (like a sort of pine tree green) and lasts a long time without fading.