The Battle Frontier in Emerald was my favorite... My favorite facility was the Battle Dome and I'd usually enter in a combination of three pokemon, one would be a mixed sweeper, another a special sweeper, then a physical sweeper. That way, I could counter every pokemon my opponent's entered, and looking at their teams helped me a lot.
The Battle Pike, I completely BS'd and just kind of went on what the lady said, like "I feel a strong aroma of pokemon" or whatever, I'd go in there. Usually, that was where that giant snaking room was full of pokemon you could run away from.
The Battle Pyramid was one of the worst. I would wander around aimlessly and try to avoid everything.
Battle Palace? I wish I could burn that place to the ground. I hate it. Palace Maven Spencer was nearly impossible since he had a Slaking and my pokemon never liked to attack it.
Battle Factory, it wasn't so bad. The first choice selections, I would choose two pokemon I knew I would use and pick a random third. I'd always trade the third, so eventually I'd battle and get progressively better pokemon. One I remember in particular was a shiny Charizard as a special sweeper. Factory Head Noland was a bit easy though, since he always had random pokemon too. But by that time, I'd always battle someone with one of the following: Metagross, Salamence,
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Battle Tower, well that's just simple. Just use a team that can check each other and that's about it. Usually, the same like my team for the Battle Dome. A physical/special/mixed sweeper. Occasionally I'd add in Suicune as a wall, and it worked wonders. Salon Maiden Anabel was a piece of cake.
Battle Arena was real easy. First turn, I'd use a Shiftry or anything that can learn Fake Out and use that. That's one turn for me. Then I'd use Protect/Detect, then finally Hyper Beam or something that hits hard. Other times, I'd just try to knock them out, but that was more toward when I first started going there when they all had NFE pokemon like a Pichu or something.
Well, that's just about it. So my overall strategy is to hit hard, hit first. I still have my Emerald with all the Gold Symbols. I dedicated a box to all my winners. One pokemon I used the most was Scizor/Ursaring (Swords Dance) and I think Latios (all-out special attacker). I think I might play it again...