1) Super Plasma Bolt -> Hold the UP arrow for about 2 seconds until you
                        hear the "charge up" noise.  Then press the
                        fire key.  You'll take a hitpoint of damage
                        doing this.
 
2) Fireballs         -> Turn left and right in sucession about 6 or 7
                        times and press the fire key.  You'll take a
                        hitpoint of damage doing this.
 
3) Shield            -> Turn left and right in sucession about 6 or 7
                        times and press the jump key.  You'll turn a
                        different color, and a shield will appear around
                        you.  This lasts a VERY SHORT amount of time.

4) Invincibility     -> Hold the up arrow at least 2 seconds, then press
                        the down arrow.  You will flash and be
                        invincible for a VERY SHORT amount of time.
 
Some hex editing will help you as well:
(This is version specific - backup first!!!)
for immortality, ulimitied bullets & bombs:

hex edit bmenace1.exe

Offset 61-64   change 2B 46 08    to 90 90 90
Offset 254-257 change FF 0E 08 44 to 90 90 90 90
Offset 117-120 change FE 0E 0D 44 to 90 90 90 90
Offset 468-471 change FE 0E ED 43 to 90 90 90 90