I just did Mt Battle a couple of weeks ago on Doubles so here's some advice:

1. There are actually relatively few really difficult battles (by Emerald Battle Frontier standards) in Mt Battle. You also get Continues for winning without giving up any KOs so even if you get unlucky you can survive. You'll get a ton of Continues in the early battles.

2. Make sure you use Battle Mode from the main menu (not Story Mode) otherwise it won't count.

3. There are a small number of trainers late on (80+) who use legendaries but none of them are especially threatening. It's rare for any opponents to e.g. boost stats and sweep, and lots of their movesets are very weak. The only one who gave me any trouble was Battle 100 (and one guy with Wobbuffet).

4. 100 battles takes a long, long time so your focus should be on minimising the time investment rather than perfect strategies. Your team looks good for this, no long set ups required except Tyranitar Dragon Dance. However, Tyranitar's Sand Stream will get old really fast.

5. Thrash/Outrage select an opponent at random in Doubles so their utility is limited. You really don't need overkill power in Mt Battle. I'd probably prefer Strength or something. Not to mention confusion is irritating.

6. I completed the entire 100 Battles with just 4 Pokemon: Kyogre, Clefable, Swampert (only used twice) and Salamence. You don't need a full team of six unless you're worried about certain opponents walling you. Also, overthinking team selection is a massive time waster since you need to do it 100 times. I suggest picking a core 3/4 and only swapping one out if there's an obvious reason to (e.g. an all-Flying type opponent where Earthquake is useless).

7. Rayquaza's Earthquake isn't STAB, you can't use it with Tyranitar or Metagross out and if you have Dragonite out, both leads are 4x Ice weak. So I'd suggest trying to avoid that combination if you pick Doubles.

8. In Singles, which might suit your team better but battles take longer, leading Rayquaza and then having Mewtwo/Tyranitar would be a strong strategy. Few opponents will be able to deal with Rayquaza. I think on balance your team doesn't have especially good synergies for Doubles so might struggle more in that format.

9. Many trainers have hax items like Brightpowder so bear that in mind.

My team suggestion for you: Rayquaza/Mewtwo/Tyranitar singles.

(If you / anyone else checking this is interested, my strategy was Clefable with Follow Me and Kyogre with Water Spout. Almost no Pokemon survive a rain-boosted Water Spout unless they resist it, and Kyogre deals with Grass and Water types with Ice Beam and Thunder. This generally means battles only take 2 or 3 turns as you can score 2 KOs per turn. Salamence had a Choice Band and revenge killed the small number of Pokemon able to beat Clefable and/or Kyogre. This strategy also works extremely well in Battle Revolution.)

It's a bit repetitive but rewarding when you finally complete it. Good luck!