At some point between How to Train Your Dragon 2 and the third movie (a span of about a year), Astrid's armor was constructed.
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Astrid's dragon scale armor appears to be formed of several different pieces tailored to fit her body. There is the helmet, pauldrons, chest plate, torso guards, a skirt-like part over the hips, gloves, and gauntlets, leggings, and boots. There are also two wing structures kept folded for flight when needed. The suit is made out of Stormfly's shed scales, so has a predominantly blue color. The scales appear to be attached to a leather base, with Toothless' sticky saliva as the gluing agent. The whole suit is further embellished with small metal skulls around Astrid's midriff, and various spikes mimicking those of Stormfly.
Due to its construction from Stormfly's scales, Astrid's dragon scale armor is effectively impervious to fire. It is unknown if the non-scale portions are also treated in some way to be fire-retardant.
Like a suit of armor, it affords some protection from attack, much better than normal clothing. However, dragon skin and scales can be cut and pierced, so the armor is not fully protective from all attack.