Yes, I have, and I routinely pound them into the ground. Maybe once a month I beat them... once through; but Shinryu I like to destroy multiple times.

There are a number of thing you can do to defeat the created monsters. First and foremost, you will want a well trained party, with at least 3 fully activated Celestial Weapons. Also have characters that have mastered at least 3 sections, and reasonably well-customized armor (+30%HP/MP, and 2 things of choice, depending on character). I will assume that you have all the Aeons in your possession. Having Wakka's Attack Reels and his weapon are the best way to beat an enemy, Auron's Bushido Blade will inflict all breaks, so that is useful, and either use Yuna/Rikku for healing and item purposes. (surprisingly enough Yuna is FASTER than Tidus and Wakka, despite people saying otherwise)

The area creations are relatively easy to defeat, and leveling up in Omega Ruins should be sufficient to defeat most of them. The species will be more difficult, but most of them are pushovers, and they drop the blue spheres that give +4 to stats, +40MP (not at ALL necessary), and +300HP (<3).

There are 8 monsters, and the easiest ones to beat are Ultima Buster, Neslug, and Catastrophe. the bonues for beating these monsters is HUGE, so for every one you beat, it will make the others 1% easier.

I apologize to the moderators, but I might have to double/triple post to give a detailed guide to beating these... abominations.