You want to catch this Pokemon, not knock it out, because if it's K.O.ed, it's gone for good, so if you have a Pokemon with False Swipe you're in good shape. Putting it to sleep is a good idea, of course.
Consider using Accuracy-reducing techniques such as Flash to improve your Pokemon's chances. Electric, Ice, Water-type attacks are all good choices to chip away at its HP, although Rock is the strongest against this Flying/ Fire hybrid. Ho-oh has tons of HP and can heal itself with Recover, so this will be a long and difficult battle. The teleporters on the seventh, eighth and ninth floors are also tricky, but if you start with the right one it's a piece of cake: on the seventh floor, walk past the first one you pass (and grab the Max Revive in the corner), turn south and head for the one all the way at the bottom of the room. The trickiest part is on the fifth floor: turning right from the upper left corner, take the first path down you come across, and head south as directly as possible (avoid detours to the right or left) and you should make it to the stairs you want in the bottom center of the level. It will take persistence to navigate the one-way paths and make it to the roof where Ho-oh awaits. The Tin Tower is a veritable maze of platforms, pits and teleporters.