I found this on a walkthrough:
At the beginning of the battle, switch Salamence for Lugia and have
Electabuzz use Shadow Half. You need to do this first, otherwise Rhydon
might use Shadow Hold to lock your Pokemon. On the second turn, have
Lugia
use a Lemonade or Moo-Moo Milk on Electabuzz to restore its HP. It's
extremely important that you keep Electabuzz alive. On the third turn,
either heal Lugia or throw a Ball at the Rhydon (catching it is important
due to its annoying moves), and have Electabuzz use Shadow Half again.
Next, have Lugia use a healing item on Electabuzz, unless it has under 30
HP. On the next turn, Moltres should be at 25% HP and Exeggutor at 50%.
Have Lugia use a Moo-Moo Milk or Hyper Potion on itself, and Electabuzz
use Shadow Half again. If Exeggutor uses Shadow End to knock out
Electabuzz or Lugia, just send out Salamence and use a Revive on it, then
switch out for it next turn. Once Exeggutor has around 15-30% HP, use an
Ultra Ball to catch it. This should be around Turn 5 or 6. Have
Electabuzz
use Shadow Half when you throw the Ball, so you'll half the next
Pokemon's
HP. Once the Tauros comes out, you'll be in good shape. Lugia will likely
be weak around now, so use a Hyper Potion on it to bring it back to
health
while you wait for Electabuzz to recharge. Next turn, Moltres will be
under 10% HP, and Tauros will be at 50%. Have Lugia use a Lemonade on
Electabuzz, and Electabuzz use Shadow Half. Tauros should be at 25% HP,
and Moltres should be very weak (under 7%). Tauros' only attack move is
Shadow Rush, so you don't have to worry about it too much. At this point,
throw an Ultra Ball at Moltres and hope to catch it. If it's under 5% HP,
chances are you're going to catch it on your first Ultra Ball. If you
don't catch it, have Electabuzz throw Ultra Balls at it instead of use
Shadow Half while Lugia heals. When the Articuno comes out, start using
Shadow Half again. Don't worry about Tauros, although be ready to
administer Ice Heals or Full Heals in case Articuno's Shadow Chill
freezes
you. Electabuzz may be knocked out again. This happens. Just remember to
send out Salamence, and have Lugia use a Revive or Max Revive on
Electabuzz while Salamence switches for it, otherwise Shadow Hold may get
you. Use the Shadow Half + Heal tactic to get Articuno down to 12.5% HP,
and then start throwing Ultra Balls at it on Electabuzz's turn. If at
12.5% HP Articuno doesn't stay in the Ultra Ball, use Shadow Half again
to
almost ensure it being caught. Once Articuno has been caught, you only
have to worry about Zapdos. Before you use Shadow Half to start hitting
Zapdos, throw an Ultra Ball to catch the Tauros while you have Electabuzz
use Shadow Half. Tauros should have less than 5% HP left and should be
caught with one Ultra Ball. With Tauros out of the picture, you only have
to worry about one attack per turn, and that's Zapdos. Unfortunately
Zapdos has very high Special Attack, causing Shadow Bolt to do a lot of
damage, but still less than Shadow Chill + Shadow Rush combined. Shadow
Half + Heal until Zapdos is at 6.25% HP, and then start lobbing Ultra
Balls at it. If Zapdos hits Lugia on the turn Electabuzz uses Shadow
Half,
you can toss an Ultra Ball at it on the next turn to hope to get lucky if
you want, because it will take two non-critical hits for Zapdos to knock
out Electabuzz at half HP. Once Zapdos is at 6.25% HP (after 4 uses of
Shadow Half), if you have a Pokemon that can inflict Sleep or Paralysis
on
Zapdos, stop healing Electabuzz and wait until it faints so you can send
that Pokemon out. Continue using Shadow Half, but have Lugia throw Ultra
Balls at Zapdos instead of healing Electabuzz. Eventually, Zapdos will
stay in the Ball, and you will have caught all 6 Shadow Pokemon in one
battle!
Cheap and Boring way:
Switch the Electabuzz for Lugia, and then just stall for about 40 turns.
Use healing items to restore your Pokemon's health, and keep track of how
many turns have passed. After 40 turns have passed, weaken all of
Greevil's Pokemon with your Shadow attacks and then throw Timer Balls
when
they're at about 50% HP. You should be able to catch all of them with
about 10-15 Timer Balls, although bring 25-30 just in case.
