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This will also come naturally as you go for Platinum as you’ll also need to visit every Island here for Checking the Gears as well as to complete the main story path. All of the Spiders can be killed in Clockwork Town. They will 99.99% of the time block your path going forward so you’ll need to kill them just to move forward in the story. When the trophy unlocks depends on what route you take through each Island, but as soon as you have killed the last Spider (the Nightmare and any minions she herself spawns don’t count for this), the trophy will unlock.