You have to have a steel frame made and secured to the wall studs from the floor up to the aquarium height. The aquarium base cantilever out.
Easiest is metal frame on the wall or if you don't want to see the metal uprights, then you have to cut open the wall and secure at the side of the wall studs.
If you know someone that is good at welding, its easier to have it built on site. Aim for 1000lb live load capacity for the cantilever is 13-14" deep, accounting for some space behind the aquarium.
An issue may be the stud spacing and the more direct the downward force from the cantilever is exerted directly on the upright support, the cheaper (not having to go up in metal gauge, cuts and welds) and easier the work will be.
HTH/JM2C