BOSS! As if she didn't have enough shields to begin with, her shields increase by 75% of the power of any attacks against her that do not kill her outright. Fortunately, this only happens for at most the first 5 shots that hit her, and sometimes fewer.
The TethysBot's ability essentially means that the first few shots that hit her do only 25% damage if their damage does not exceed her remaining shields. It may be tempting to waste her ability on shots from weak weapons such as the Pistol, but her high damage and range make this a bad choice. Assuming no weapons capable of a one-hit kill are available, the best way to deal with her is to hit her with long-range, medium-strength weapons such as the Gamma-Ray Laser or a suitably upgraded Laser Rifle to wear down her ability, then hit her with your strongest weapons. Mines, Sentry Turrets and electrified floors all also work for wasting her ability uses.