How is aqua regia stored as it dissolves all metals?
No one stores aqua regia for extended periods, because it decomposes rapidly, yielding volatile products that escape from the solution resulting in a loss of potency.
From the Wikipedia article on aqua regia,
Due to the reaction between its components resulting in its decomposition, aqua regia quickly loses its effectiveness (yet remains a strong acid), so its components are usually only mixed immediately before use.
The mixture itself is created by combining $\ce{HCl}$ and $\ce{HNO3}$ in a 3:1 molar ratio in glass vessels immediately before use.
Aqua regia doesn't readily react with glass. So while you could keep it in a glass retort for years, it would be nothing like the original mixture (you be hard pressed to even call it "aqua regia" after a day, much less, after a few years).
A famous incident in this regard, was when de Hevesy dissolved two gold Nobel medals in aqua regia to hide them from Nazi Occupiers, and kept the solution in a glass retort on a shelf and returned to collect it after about 5 years (the bottle was still intact)
When Nazi Germany occupied Denmark from April 1940, during World War II, de Hevesy dissolved the gold Nobel Prizes of Max von Laue and James Franck with aqua regia; it was illegal at the time to send gold out of the country, and had it been discovered that Laue and Franck had done so to prevent them from being stolen, they could have faced prosecution in Germany. He placed the resulting solution on a shelf in his laboratory at the Niels Bohr Institute. After the war, he returned to find the solution undisturbed and precipitated the gold out of the acid.
Also, your question assumes that all metals are dissolved in aqua regia, which is apparently, not the case, as discussed under this post.