>>48254377Depends on the facility. This smogon thread is a good resource to get started though.
https://www.smogon.com/forums/threads/gen-iii-battle-frontier-discussion-and-records.3648697/I'm gonna assume you only have access to Emerald.
Latios, Latias, Metagross, Salamence, Swampert, Milotic, Registeel (if you can do TrickBand shenanigans to let it set up), Alakazam, Slaking, Heracross, Medicham, and Starmie are all solid picks.
For the Arena, you might give attention to things that can cripple (Breloom spore etc).
For the Palace, you need to take into account your pokes' natures and moves (Psypokes has a good page on it).
For the Pyramid and Pike, you probably want something that can run away if possible, or otherwise just waste wild pokes, as well as a cleric (a lot of people use/will suggest Blissey but you'll need to trade FRLG or inject if on ROM).
For the Tower, no gimmicks, just goodstuffs will do.
For the Factory...good luck.