Our original solution used Cursed Stone to change Stadium cards. But the wise players solving the puzzle on the Web have noted that our solution adds unnecessary steps! Instead, you'll get two Prize cards for knocking out Lugia ex. So, the name "In Between Dreams" is kind of meaningless since you win on your own turn! Thanks to the players on the PokéGym for keeping us honest and making us better players!
Before attacking
--Put Cursed Stone into play, discarding Battle Frontier
--Attach Multi Energy to Mew ex, making each of them produce Colorless Energy
--Use Switch to make Mew ex your Active Pokémon and put Regirock ex on your Bench
--Use Pow! Hand Extension to switch your opponent’s Latias [star] with Lugia ex from the Bench
Now you’re ready to attack. Mew’s Poké-Body let’s you use any attack in play, so...
--Mew ex uses the Clutch attack from Pidgeot to do 40 damage to Lugia ex. (The attached Holon’s Magneton gives it enough Energy to do so!) Lugia ex has Weakness to Psychic Pokémon, so Mew ex’s attack does 80 damage, Knocking Out Lugia ex. You get a Prize card.
Lugia ex allows your opponent to flip a coin to see if Mew ex will lose an Energy card, but it doesn’t matter. After your turn is over but before your opponent’s begins, Cursed Stone has you and your opponent put 1 damage counter on each Pokémon in play that has a Poké-Power... and that’s only Pidgeot, which can only take 10 more damage before it’s Knocked Out.
So, in between turns, you take your second Prize card and win!