Quote from PandaBennington Randomly [on a
random page, not just the quest page] Giratina will pop up on your
screen, the first time you must click 5 of them in X amount of
time. The second time you will have to click 10 in X amount of
time. The third time you will have to click 20 in X amount of time.
And finally you will have to click 100 in X amount of time. You
will then receive a [Spooky Manor] map that you have to send a
Pokemon on a rumble for [one time use], it will bring back a
'summon' item that you can then go to the Ancient Cave and trade
for the Giratina egg. *You must have an empty space in your party
to obtain it!* [It will also break your chain]
So you just have to keep visiting pages randomly until the Giratina
minigame(s) appear.