Would you max out this shiny Aggron?

If you have nothing better to upgrade sure, go ahead. I'm swimming in dust often here, but I always get stuff to level before shinies so I never got around to leveling any shinies.

I never powered up any of my 5 shiny Aggron because none of them have good IVs. I take it that you biome is similar to mine and you are bound to find a perfect one soon. Aggron being the king of autoselect, you would benefit from only maxing out a very, very good one and be done with that species.

So I would only power it up if it had good IVs, above 96%

I would never power up an Aggron. It's not meta relevant and it is already too annoying getting it suggested in every pre selected team when you raid or attack gyms...

For a trophy yes, but if u want it to be meta relevant then sadly it's not. Used one once as 6th man in a Jynx raid but never got that far. Also super annoying on auto select so best use for em is to put em in gyms then leave em dead.

If you have extra dust that you dont need sure.

Aggron is pre-selected in many battles due to its great base stats and a shiny one would look nice as well even if its just for fun.

(and no the arent annoying as someone else posted, they are useful which is why they are pre-selected)

Though I've been known to power up non-meta Pokemon (Muk, 100% Cradily), I would pass on Aggron. It's just not a fun Pokemon. Its "quick" moves are slow, its charged moves aren't inspiring, it will get autoselected for EVERYTHING when it isn't good at ANYTHING, and it's a paper tiger in gyms.

Pass.

I wouldn't power up a shiny Aggron if it were perfect. Aggron is pretty poor while attacking, and it's strong defense is neutralized by a double weakness to Fighting (who doesn't have a Machamp to attack it with) as well as Ground. One of the most disappointing pokemon to date.

Personally, I have two Aggrons, both were caught as strong high level Arons, and evolved, no dust invested. They are fairly useless.
There could be a use for them as a steel attacker, once something that is doubly weak to steel comes up, but Metagross, Magnazone, and eventually Dialga are/will be much better. Save your dust unless it really makes you happy to put it into a shiny Aggron.

I have a 100% Aggron maxed. I keep it at 0hp like all my other Aggrons so I don't have to see them in my autoselect. Wouldn't recommend investing resources for anything except trophy reasons.