You'll be getting this on your way to "High Score". Check that acheivement description for an additional strategy to defeat Jet. Prior to the fight, try and collect the extra lives and accumulate enough for about 3-4 lives by the time you get to the fight. Watch out for her goons and the second jet character called Tomcat. One of the best ways of taking these flying characters out is by letting them fly across the screen, jump kicking them, back off and then rinse and repeat.
**Something that will help for the "High Score" and "Kill Jet" achievements is that you can save at any time during the game, so save it constantly. Even after every group of enemies, it may take a while but will make this easier.
If you just can't get this, you can always resort to the trick outlined in the Roadmap.