You're looking for something that basically kills everything without being killable? Doesn't exist afaik.
The closest thing to this that I've seen in my walk-through, is Speed Miko. High Fo.Atk, moderate speed that gets boosted every turn. Only the very fastest puppets can outspeed Speed Miko for more than one turn. Her moveset includes several attacks of 120 power 100 accuracy, but 1/3HP drawback. Besides these, High Tone Crush does the job most of the time. Oh, and she can self-defend against Wind types with Spark Javelin.
Basically, Speed Miko is THE way to go if you want high power, top speed and wide coverage. But you have to pay this with a chance to be outsped in the first turn, as well as HP losses for the 120 power attacks.