How to go about building an aquarium into a wall?
I am not a licensed carpenter but I have replaced walls and doors in my old house. Here is how I would do it. 

I think you should not try to use a cantilevered or bracketed shelf for this. Make a strong table to hold the aquarium. 

In the following I am assuming wood construction, with your walls made of the usual 2"x4" studs and wallboard. 

The front edge of the table can rest on the bottom edge of the opening, with the back edge resting on four legs. 

When you make the opening, cut the lower studs 4 inches shorter than the finished opening, and frame the lower edge with two 2"x4" standing on their short sides. This forms the front edge of the table frame. Don't worry if the ends of the edge don't line up with the studs. 

EDIT The single 2"x4" studs may not be strong enough to serve as legs for such a heavy load. You should add more short studs by inserting them into the lower wall and nailing or screwing through the drywall. If the boiler side of the wall is unfinished then you can toenail the new studs but this is not strictly necessary.

Make two of the new studs line up with the ends of the front edge. You should have eight studs in all under the front edge. END EDIT

Make the side and back edges of the table frame similarly of paired 2"x4" nailed or screwed together. 

The surface of the table can be of lighter construction because an aquarium rests on its own lower edges. The table surface serves mainly to keep the frame rectangular. 1/2" plywood should be enough. 

The legs can be more paired 2"x4" or single 4"x4" each. Use four legs evenly spaced along the back edge. 

Here is a rough sketch of what it might look like from the boiler room:



EDIT As Kyle points out, this sketch is incomplete. I have not drawn in the table top, the leg bracing, the header at the top of the wall opening, or the finish framing of the wall opening. END EDIT

You will have to figure out a way to keep the bottoms of the legs from being accidentally moved during any future work in the boiler room. In my house I would use a sill plate nailed directly to the concrete floor. You might want to use angled braces from the frame to the foot of the legs. Make the braces of 1"x3" or 1"x4". 

Give the whole construction a couple of thick coats of paint to keep the splashes from soaking the wood and starting wet rot.