How did whoever make that think you would filter it?
You essentially have a sump at the back, but no real way of circulating water from the sump into the seperate compartments at the front and nowhere really to hold filter media.
You could have seperate return pumps and return nozzles for each compartment, so that each compartment gets water circulation, and then just dump some bagged up bio media in the sump and hope for the best. That would provide no mechanical filtration though, and you might want a powerhead in the sump to try and get water flow around the sump and through the bagged up bio media.
Maybe something like K1 filter media in the sump would work?
You could do each compartment with a seperate internal, HOB
or sponge filter, but then the rear sump is doing nothing.
You could get some media trays made for the sump, fill the trays with biomedia and sponges, position them so each drain goes into a tray, then return pumps sit next to tray and return water to each compartment. You could get the trays 3d printed. Something like one of these that can go in the rear sump of a fluval flex.
Really stumped on an easy to filter this, hopefully someone else has a better idea or has seen something similar.
When you say it was made by your local aquarium, do you mean aquarium store or an actual public aquarium made it? Either way i'd ask them how they envisioned it being filtered, and if it isnt what you wanted id look at getting the cost refunded in some way.