From StrategyWiki, the free strategy guide and walkthrough wiki

Neo Contra has several different endings, which one you get is determined by your average ranking and the end of stages 4, 5, 6, and 7.

[edit] Part I: The Contra Commanders

These stages are available in both easy and normal modes and can be completed in any order. Your mission in each stage is to assassinate the Contra Commanders, one at a time. All that stands in your way is the entire Neo Contra army. Along the way you'll meet a rather odd ally as well as an old friend of Bill.

• Stage 1: Base 985
• Stage 2: The city
• Stage 3: Mountain pass
• Stage 4: Airship

[edit] Part II: Red Falcon

In order for stage 5 to be unlocked, you must have an overall ranking of C or higer in normal mode. It wouldn't really be a Contra game without Red Falcon, would it? He's back (sort of) and is in need of some good old fasion killing.

• Stage 5: Alien lab

[edit] Part III: Project C

You will automatically move from stage 5 to stage 6 if you overall ranking is B or higher. Likewise, you will only move to stage 7 if your overall ranking is A or S. Having disposed of the rest of Neo Contra, it is time to take out the leader, Master Contra. Kill him and the truth will reveal it's self - just not in the way Bill was expecting.

• Stage 6: Neo Contra Headquarters
• Stage 7: Project C