The key is to learn the backwards alphabet as "words" rather than individual letters. If you break it into chunks of 4 letters (with 2 left over) you have:
ZYXW VUTS RQPO NMLK JIHG FEDC BAPractice saying this as you write each set of letters one after the other. With a little practice you'll be able to write this very quickly.
Phonetically think of this as the phrase:
"Zixwa Vuts Irqpo Nimlick Jig Fedic Bah"
Now you are ready to challenge your friends to a race. You can even bet them that you'll write the alphabet backwards faster than they write it forwards. The reason it works is you won't need to stop, think, sing that alphabet song, go back a few letters, etc. You simply write down your 7 "words" as quickly as possible and you are sure to beat them.