Human-Fish acts typically featured performers who could stay underwater for long periods of time. The act would usually be performed in a tank with glass sides for observation, and performers would do things like eat, drink, smoke, sleep, juggle, shave, sing, etc. while submerged. A breathing tube was usually secreted into the frame of the tank, and the performer could thus almost indefinitely stay submerged and performing by surreptitiously taking a gulp of fresh air when needed.
The act itself was awkward as performers had to transport the heavy tanks over the roads or rails, fill it for each performance with fresh water, often heat the water, and hope the tanks didn't leak onto the stage of each venue they played.
A similar act is still famously performed today at Weeki Wachee Springs State Park in Florida, where women in mermaid costumes perform much the same act as vaudeville and circus performers did going back to the 1880's.