You get the first gauntlet by taking the aptitude test with Akane. You need three strength after finishing training strength with her (she offers you to take the aptitude test if you level up to 3 after training with her, otherwise you'll have to train strength with her after you're at level 3 or higher. I think, I haven't tested the second part). After she offers you the aptitude test, visit the dojo at night and you'll be able to take the test. Pass the test and you get the first set of gantlets.
To get the second set you need to toss the gantlets and 5 goddess coins into the upgrade pool that is hidden in a cave to the right of the library. You need to first set of gantlets to punch a hole in the cave wall there. You can similarly upgrade the shovel but nothing else (at-least yet).