A whip like particle system

As far as I know, it's not directly possible with the particle system. You will need to have the whip animation from somewhere else, 3D app for instance. You need a set of points forming a path moving over time like a whip.

In 3DSmax, I would use bones to move points helper, then on Unity retrieve those points in an array in the correct order (from the first, the handle of the whip, to the last).

Then, you need to shoot x particles at once, get the array and position them manually along the path, sort of like the procedurale example of lightbolts.

Good luck !