Allura will choose Ampharos, Tyranitar, and Blissey.
Allura will start out with Ampharos and Thunder Wave first, given that two out of three of Sion’s Pokémon are Flying types and Typhlosion has no resistance to Electric or paralysis either. The paralysis will also mess with Archeops’s Speed advantage over Ampharos and how many attacks he can land, giving Ampharos time to set up Confuse Ray (given that paralysis and confusion are non-volatile and volatile, respectively, they can stack) before Thunder and Power Gem, barraging Archeops from a distance and refreshing the status conditions as necessary, keeping Ampharos healed in case Archeops manages to land something like Endeavor. (Although with Static, Archeops will probably want to avoid contact moves anyway.) Still, Roar or U-Turn might throw Allura’s rhythm for a second if Archeops manages to pull one of them off. In the former case, she’ll let her new Pokémon get in a move (Rock Slide, Ice Beam, Sing in Archeops isn't currently paralyzed, etc.) before switching Ampharos back in; in the latter, she’ll proceed to one of the strategies below until Archeops is brought back in and continue from before.
For Typhlosion, Allura will bring out Tyranitar. Not only is there a good type advantage with Rock vs Fire, but Tyranitar will turn out to have considerably higher stats in everything but Special Attack and Speed, and the Sand Stream Ability should whip up a nice sandstorm for a little extra damage per turn, lowered accuracy, and making Solar Beam slower and much weaker. Since Tyranitar doesn’t have any status moves, Allura will start off with Screech to lower Typhlosion’s Defense before wailing with Rock Slide, Earthquake, and Ancient Power, with Rock Slide having a flinch chance and Ancient Power having a chance to raise all of Tyranitar’s stats by one stage. Since Typhlosion doesn’t have any switching moves, the only moves that could really cause a problem would be Toxic (if Tyranitar isn't burned first) and Smokescreen. For the former, Allura can use an Antidote, but if Smokescreen lowers Tyranitar’s accuracy to the point she can’t land any attacks, Allura will switch to Ampharos and continue the same strategy he had with Archeops.
Finally, Allura will choose Blissey versus Pidgeot. She’s a bit more familiar with Pidgeot’s strengths and weaknesses thanks to her battle with Falkner, and not only is Blissey neutral to Pidgeot’s typing (and, coincidentally, all of the Bird Pokémon’s attacks), it looks like she has some nice super-effective special attacks in her arsenal, as well as healing moves to keep her tremendous HP pool in tip-top shape. So Allura will have Blissey start off with Sing to make Pidgeot fall asleep, then Minimize to raise her evasion (which should thankfully work since Pidgeot has Tangled Feet instead of Keen Eye). Once that's set up, she'll hit the birdie with Thunder and Ice Beam, both of which have status effect chances which are doubled thanks to Serene Grace, adding Flamethrower to the mix if Pidgeot uses Roost and isn't already frozen, so that’s high chances of Pidgeot being frozen, burned or especially paralyzed if the Bird Pokémon wakes up. The only troublesome moves of Pidgeot's are Hurricane, U-Turn, and Whirlwind. If Hurricane manages to confuse Blissey, she does have a low-enough Attack, high-enough HP, and healing moves that confusion damage shouldn’t be too strong, as well as a high Special Defense to endure Pidgeot’s onslaught since all of her attacks but U-Turn are special instead of physical. In case of U-Turn (if Sion’s other Pokémon are still standing), Allura will have Blissey Sing at them before switching to one of the above strategies (save for Tyranitar not using Earthquake against a Flying Pokémon, of course); for Whirlwind, Allura will let the new Pokémon let off an attack before switching Blissey back in.
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Allura will choose Ampharos, Tyranitar, and Blissey.
Allura will start out with Ampharos and Thunder Wave first, given that two out of three of Sion’s Pokémon are Flying types and Typhlosion has no resistance to Electric or paralysis either. The paralysis will also mess with Archeops’s Speed advantage over Ampharos and how many attacks he can land, giving Ampharos time to set up Confuse Ray (given that paralysis and confusion are non-volatile and volatile, respectively, they can stack) before Thunder and Power Gem, barraging Archeops from a distance and refreshing the status conditions as necessary, keeping Ampharos healed in case Archeops manages to land something like Endeavor. (Although with Static, Archeops will probably want to avoid contact moves anyway.) Still, Roar or U-Turn might throw Allura’s rhythm for a second if Archeops manages to pull one of them off. In the former case, she’ll let her new Pokémon get in a move (Rock Slide, Ice Beam, Sing in Archeops isn't currently paralyzed, etc.) before switching Ampharos back in; in the latter, she’ll proceed to one of the strategies below until Archeops is brought back in and continue from before.
For Typhlosion, Allura will bring out Tyranitar. Not only is there a good type advantage with Rock vs Fire, but Tyranitar will turn out to have considerably higher stats in everything but Special Attack and Speed, and the Sand Stream Ability should whip up a nice sandstorm for a little extra damage per turn, lowered accuracy, and making Solar Beam slower and much weaker. Since Tyranitar doesn’t have any status moves, Allura will start off with Screech to lower Typhlosion’s Defense before wailing with Rock Slide, Earthquake, and Ancient Power, with Rock Slide having a flinch chance and Ancient Power having a chance to raise all of Tyranitar’s stats by one stage. Since Typhlosion doesn’t have any switching moves, the only moves that could really cause a problem would be Toxic (if Tyranitar isn't burned first) and Smokescreen. For the former, Allura can use an Antidote, but if Smokescreen lowers Tyranitar’s accuracy to the point she can’t land any attacks, Allura will switch to Ampharos and continue the same strategy he had with Archeops.
Finally, Allura will choose Blissey versus Pidgeot. She’s a bit more familiar with Pidgeot’s strengths and weaknesses thanks to her battle with Falkner, and not only is Blissey neutral to Pidgeot’s typing (and, coincidentally, all of the Bird Pokémon’s attacks), it looks like she has some nice super-effective special attacks in her arsenal, as well as healing moves to keep her tremendous HP pool in tip-top shape. So Allura will have Blissey start off with Sing to make Pidgeot fall asleep, then Minimize to raise her evasion (which should thankfully work since Pidgeot has Tangled Feet instead of Keen Eye). Once that's set up, she'll hit the birdie with Thunder and Ice Beam, both of which have status effect chances which are doubled thanks to Serene Grace, adding Flamethrower to the mix if Pidgeot uses Roost and isn't already frozen, so that’s high chances of Pidgeot being frozen, burned or especially paralyzed if the Bird Pokémon wakes up. The only troublesome moves of Pidgeot's are Hurricane, U-Turn, and Whirlwind. If Hurricane manages to confuse Blissey, she does have a low-enough Attack, high-enough HP, and healing moves that confusion damage shouldn’t be too strong, as well as a high Special Defense to endure Pidgeot’s onslaught since all of her attacks but U-Turn are special instead of physical. In case of U-Turn (if Sion’s other Pokémon are still standing), Allura will have Blissey Sing at them before switching to one of the above strategies (save for Tyranitar not using Earthquake against a Flying Pokémon, of course); for Whirlwind, Allura will let the new Pokémon let off an attack before switching Blissey back in.