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This part of IGN's Zelda: Breath of the Wild wiki guide will walk you through how to farm Star Fragments. This material is very important in BotW, as it is necessary to upgrade your armor to its max level at the various Great Fairy Fountains around Hyrule.
In this guide, we will walk you through an easy step-by-step way to farm Star Fragments.
Remember that Central Tower has Guardians at it's base, so be careful when warping there. Also, monsters come out at night so use your paraglider or switch to your Dark Armor Set (Dark Hood, Dark Tunic, and Dark Trousers) so you can run faster.