The Rainbow Barrier is one of Annie Hamilton's special techniques, having only appeared in one game. Basically, Annie would sweep her arm downward through the air, leaving behind a rainbow-like trail of energy in its wake. It can provide defense against incoming attacks, on both the ground and in the air. This special move was only featured in the first Power Instinct.
The canon reason as to why Annie stopped using the technique after the first Goketsuji tournament was because she saw Otane in her youthful form performing the "Koushokuheki" technique, which is basically the exact same as her Rainbow Barrier. Because Annie prefers her that techniques are unique to her, she quit using it.
It's possible, however, that she changed it up to create the Rainbow Rise technique in its place, which proved to be an effective trade off.