This isn't a very hard achievement. It is easier to accomplish against enemies with a lot of health as the combo window is fairly small. This can be done several ways.
One way is to chain Mystic Arts. I used a controller for this game so I had to hold LT while swapping characters ending with Magilou who's 3rd Mystic art gets 50 hits on its own.
The regular way would to be just to build up your combo.
1) Find your opponents weakness and set up an art combo that exploits those weaknesses.
2) Fill your Soul Gauge
3) Defend until you get the 2nd red flash to guard break and use your combo until your soul gauge is low
4) Use Soul Break to extend your combo
5) After the Soul Break Finisher quickly re-use Soul Break to continue your combo.
If you are lucky you will stun enemies during the Soul Break which allows you to continuously keep using it.