If I attach Island Challenge Amulet to a Pokemon-GX that has less than 100 HP left and it's Knocked Out, does my opponent take only 1 prize?
No. You only get the reduction in Prize Cards taken if it is Knocked Out by damage from an opponent's attack.
Source: Cosmic Eclipse FAQ (2019-10-18), TPCi Rules Team (2019-10-31)

Relevant cards

Note: All applicable cards may not be listed below.
SM12_194
SM12_194
SM12_265
SM12_265