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This will come naturally as you go for Platinum as you’ll need to visit every Island for Seeking Inspiration as well as to progress through the story. Make sure you kill every Plague Rat you come across except for the Yellow-ish Plague Rat that appears in Bright Planes (the one in the area with the Flute) as well as the Yellow-ish one that appears in the Overpass of Originality (when you have to turn on the green windmill so you can get the Blue Battery for Memory V). These two can’t be killed, but all the other Rats can. When the trophy unlocks depends on what route you take through each area, but as soon as you have killed the last one, the trophy will unlock.