From the beginning of Chapter 5 onward, upon attempting to travel to Nine Wood Hills’s North Promenade, Reynn and Lann will be invited to the Coliseum. Here, they can fight against teams of Mirages for prizes. You can gain access to more battles by progressing through the main story, defeating enemies and Mirages in the main story, and completing Intervention Quests. Note that no EXP is gained from winning these battles, but there are plenty of other rewards on offer!
Preparation Is the Key to Victory
The later stages of the Coliseum have enemies that reach Level 80 and beyond! Having Lann, Reynn and all of your Mirages around the Lv. 65-75 range is a good idea before tackling them. This goes for your Mega Mirages, as well.
Speaking of Mega Mirages, if you want to have an even easier time of things, get your bahamut Mega Mirage to at least Lv. 60, complete his Mirage Board, and give him Magic+++. Megaflare is already no joke, but with those stats behind him, his damage potential approaches ridiculousness.
Good places to grind for levels to take on the later Coliseum battles are the EX Dungeons, which open up after you beat the Postscript. If you haven’t cleared the Postscript yet, another excellent place is the Secret Ice Ridge location in the Ice Ridge dungeon. It’s the area that opens up during the Vestiges of Life quest (where you obtain Tamamohimé).
Wait until You’re Ready
As a general rule, hold off on entering a Coliseum battle unless your party is close in level to the team you’re planning to fight. Going in underleveled is a good way to have a bad time, to the point where even a strategy guide won’t help you!
That said, losing doesn’t carry any harsh consequences—you’re just warped back to the front desk as if nothing happened.
Imprisms A-Plenty!
The Coliseum is a great place to imprism a wide variety of Mirages. However, many of them come in stacks, so you’ll have to use stack-toppling abilities to topple them and imprism the Mirages individually. For machines, be sure to bring eldboxes, as well.