A monster fight happens when two species not only dislike you but dislike each other. You will notice one appear when you use the encounter circle and get two monsters in range. If their names appear in yellow, you have a monster fight on your hands where it is a big free for all. The achievement stipulates that you must only make these fights happen, not actually win them. Best way to do it is near Jibral, get a Chief Rolling Ripper (Beetle like) and a Cockatrice (emu like) in one battle circle and then attack and then flee. Rinse and repeat. 100 will take you less than an hour. Can also get the "50 Flees" achievement at the same time. You can keep track of how many you have done in your battle record.