As Dr Coyle has played a very important role in the world of Arms as she is the director of Arms labs and has created Helix, Hedlock and Springtron.
She's the director of ARMS Laboratories, and a certified genius. Fascinated with ARMS since she was a young girl, Dr. Coyle decided early on to devote her entire life to ARMS research. Her plans for this research are not necessarily nefarious... She simply wants to be the most powerful ARMS fighter of all time...even if that means subjecting herself to her own experiments. But all her pain and hard work will be worth it if she wins the ARMS Grand Prix! - Arms website
She also has a large rivarly with Max Brass for the above mentioned reason (Her wanting to be the most powerful.)
Now while Arms doesn't have a straight up villain, I think this is possibly the closest we're gonna get to an actual antagionist in the series.