>>6975342Anon, you could build yourself a tank that has similar pressure to the deep sea without too much effort or money. It might not be great to maintain but you absolutely can do it.
Given that you'll have to maintain constant pressure to bring the animals above water, you're best bet would be to assemble the aquarium in the deep sea, put the animals in there and bring the entire thing up to the surface.
There are also certain creatures under the ocean that can actually survive normal ocean pressure so your best bet would just be to go for those.