The person hiding in the mirror was Illuso from the Hitman Team. Fugo ends up being dragged into the mirror by Illuso's Stand, Mirrorman. Fugo then summons his own Stand, Purple Smoke. Despite Giorno wanting to find Fugo, Abbacchio decides to go look for the key, since that was their mission. However, once Abbacchio finds the key, he also gets dragged into the mirror world...
He then figured out the 
enemy's ability from that,
...ومن ثمّ اكتشفَ قدرة العدوّ من خِلال ذلك
Davon hat er dann auf die Fähigkeit
des Feindes geschlossen.
Debió descubrir
el poder del enemigo gracias a eso.
Debió descubrir
el poder del enemigo gracias a eso.
Il a percé le mystère
de son pouvoir,
Deve aver capito il potere
del nemico da quel dettaglio,
Então ele deduziu o poder
do inimigo a partir disso,
Он догадался, что за сила у врага,