The six robots and their weapons are as follows:
Bebop Man: BLUE SHIFT
Bio Man: DNA DESTROYER
Blackberry Man: TELEGRAPH SWITCH
Craps Man: ODDS FINDER
Minus Man: ALPHA DECAY
Stagecraft Man: WORD SWORD
Each weapon clues some kind of wordplay operation that can be carried out on exactly one of the names of the other robots in order to produce a new word. This gives rise to a cyclic order of the six robots: Bebop Man's weapon defeats Bio Man, Bio Man's weapon defeats Stagecraft Man, etc., as follows:
BLUE SHIFT: Shift all "colors" (ROYGBIV) one space in the direction of
violet on the spectrum.
BIO → IVY
DNA DESTROYER: Remove all DNA bases (ACGT).
STAGECRAFT → SERF
WORD SWORD: Prefix S to the beginning of the word.
CRAPS → SCRAPS
ODDS FINDER: Extract only the letters in odd position in the word.
BLACKBERRY → BAKER
TELEGRAPH SWITCH: In Morse code, replace dots with dashes and vice versa.
MINUS --/../-./..-/... → ../--/.-/--./--- IMAGO
ALPHA DECAY: Reduce the atomic number of all chemical symbols by 2.
BeBOP → HeLiCAl
Take these six words (IVY SERF SCRAPS BAKER IMAGO HELICAL) and insert them in the given boxes. There are two five-letter words, but you can discriminate which word goes in which box by the cyclic order of the robots.
As indicated, add paired letters mod 26 (A=1) and put the result in the circles in the center to spell out WILY COYOTE, the supermeta solution for the Mega Man gameworld.