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Enter the Battle Tree, a competitive all-in postgame filler that pins you up against the toughest of the tough—it is the final obstacle that blocks the goal - the moon that blocks the sun, to be witty.
... but it's not all sunshine and rainbows here, honey. With greats like Cynthia, Blue, Red, and Wally roaming free, high-profile legendaries by any peak streak, the seemingly-rigged AI, and the pestiferously toxic—and equally annoying—strategies they harbour, the huge, verdant evergreen is by all means a troublesome maze that perhaps not even the champion of Alola themselves can conquer. So I'll help you be the conkerer of that tree. Geddit?
Step I: The TeamEdit
As the most crucial slots of the three, your first slot should encompass all facets of any reliable lead: the stat distribution, typing, moves, the like. Whatever Pokémon is chosen here will appear in any game no matter what—contrary to popular belief, in the Battle Tree you a) cannot choose your lead and b) cannot see the opponent's team. So your lead should fare well in most match-ups.
So how do you do that? Simple. You pick something with one single weakness (or two, but there are few Pokémon that make a reliable lead and have two weaknesses). Why? Because if you have one weakness you're only weak to one type, and if you're only weak to one type you're only in a bad match-up roughly one eighteenth of the time (considering the fact there are eighteen types. That figure is rather optimistic, but you get the idea). That means you're not forced to pivot into one of your other two buddies, you can hold your own against most opponents. If you picked something like Exeggutor or Aurorus as your lead, for example, you'd have to switch into another Pokémon just so many times they'd be rendered nearly dead-weight, as they only perform well against such a restrained number of Pokémon because of their many, many weaknesses. This characteristic alone already makes a lead viable. Just don't pick something horrible, like Wormadam-Trash form. While it has one weakness, its name enough about it, thanks.
Secondly, you'll want it to run recovery; good recovery means good longevity, and if you already outperform the majority of Pokémon on the other side of the field, whenever you find yourself in a weak position, being able to recover right back up terrifies the opponent; it stops that euphoric feeling of "finally, that gosh-darned thing is finally down ..."—you want your opponent to be at a nigh pressure point throughout the entire game, and having a lead that does that for you is more you could ever want. This somewhat throws options like Eelektross and Forretress out the window, since both have mediocre longevity and lack of reliable recovery. Rest is horrible, period. But, equally, reliable recovery isn't required—it's incredibly useful, but costs you a moveslot, and if you're going for an-all-out offensively-inclined lead, it's usually a waste of one.
Finally, you want your lead to be both defensively—as covered by the above two paragraphs—and offensively potent—whether it's through raw power or boosting moves, it's whatever ices your cake. As opponents for whatever reason have a regular inability to pivot their Pokémon, being able to safely set-up in a comfortable situation without the opponent being able to bring you down is fantastic, and furthers the pressure point out of the realm of vision. Again, this isn't required, but is very optimal in many situations. If you have one weakness, opponents often lack anything to touch you; if you can heal up, any damage dealt can be easily patched up and remedied, to stop the opponent from bringing such a nigh threat to the oblivion of a KO; and if you can set-up, exploiting your near-always good match-up and the opponent's inability to switch out in the vast majority of times—*breathes in*—then you're set; you, my friend, have a good lead. Well done! You've passed the hard part.
Oh yeah, you're first slot is most likely your best Mega slot, too, since Megas are by general consensus the stronger Pokémon and your hardest-to-check Pokémon could use the extra power boost. If something else already has a Mega Stone and isn't your Slot I, don't bother changing your stuff around. So long as it uses it well you're good.