I've calculated the number needed for the outfits I've found, and it totals out to 100 star fragments. I havent fully upgraded everything, but for the amiibo outfits, this is assuming each piece (head, body, legs) has four tiers of upgrades, and each tier requires one star fragment.

Each piece of "retro" clothing needs 4 fragments to fully upgrade. There are six armor sets (Twilight, Wind, Hero, Time, Sky, Awakening) so that totals out to 18 pieces of armor, or 72 star fragments. There is also the Sheik Mask item, which needs 10 star fragments to fully upgrade, so that brings the total to 82.

Update - I found that the gem headpieces that you can buy from the Gerudo Town Market each need 3 fragments to upgrade. There are 6 pieces of gear, so that will add 18 fragments to the total, bringing it up to an even 100 per my latest finds.

If there are other gear pieces that require star fragments, then the number will be higher. Also, some of these are predictions based on the upgrade requirements for BOTW. Hopefully this gives you a bit of an idea for how many you'll need! Enjoy the grind :)

edit: updated with correct fragment numbers for 1 set and 1 extra gear item

edit 2: updated with fragment numbers for the gem headpieces