Befriend Don Tonberry, a rare monster that can be found in Bresha Ruins AF100 a little to the west of the area where Atlas stood in Bresha Ruins AF005. Like other rare monsters, he will appear as a "void" before he is engaged.
Turning on the "Battle Mania" Fragment Skill will increase the odds of rare spawns and hasten his appearance. Battle Mania can be unlocked via the Chocobo Girl in Serendipity after earning the "Paradox Professor" Fragment from City of Academia AF400, which requires 100% Map Completion for all areas in the game.
Additionally, turning on the "Monster Collector" Fragment Skill will increase the odds of befriending monsters. Monster Collector can be unlocked via the Chocobo Girl in Serendipity after all Fragments from Vile Peaks AF010 & AF200 have been earned.
You can feel free to battle Don Tonberry on Easy Difficulty; it will increase the odds of your victory and will not adversely affect the odds of befriending him. If you do not befriend him the first time, wait until he spawns again and continue to battle him over and over until he is recruited; it took me 3 tries without Monster Collector.
Encounter a Don Tonberry in the Bresha Ruins 100AF which is found late in the game, when you encounter him, highly recommend you have a strong and durable Sentinel, the Don Tonberry turns his knife purple which causes him to deal huge damage, wait for that to go away then continue fighting him and repeat that, to get this trophy, you don't defeat the Don Tonberry, you tame him, I tamed him after encountering him, my first time.
I fought it during the story and wasn't expecting to catch it and I didn't, and never saw it again. Completed story, activated Battlemania and it spawmed pretty fast. Beat it and got the crystal so I guess I was lucky to get it in my 2nd encounter. I also have Monster collector ON of course. I used a simple SYN x 3 at the start with Yakshini and got ultra buffed in a single round, then switched to RAV RAV SEN with the Maxed Silver Choccobo as SEN and the fight was pretty easy, easier than the normal Tonberry which is harder to stagger. When he inflicted poison I switched to COM MED SEN for fast removal and after staggering it just kept going and switched to COM COM SEN. 35 seconds later the crystal was mine.
Took me about 15 tries as well. If you've got fully levelled Serah and Noel (with Noel's strength over 1,000) there's no real point using sentinels or medicals. Just RAV/RAV/RAV and COM/COM/COM did the trick for me.