Open up the wall, if you have the carpentry skills, and add bars called flexible channels or resilient channels to the studs. While these connect to both the drywall and the stud, they allow the stud and drywall to remain unconnected to each other -- you connect the drywall to a point on the channel that’s a little bit away from where the channel connects to the stud. This creates a break in the material and thus a break in the flow of sound or reverberation. The drawback to this method is that you’d have to remove the drywall completely and likely replace all of it rather than reuse it, not to mention you'd have to paint the walls afterward. Because you are changing the way the drywall and wall interior are connected, you would also have to clear the process with your condo’s homeowner association, your city’s planning department, your insurance agent and probably your neighbor.
Metal is an efficient transmitter of sound, and that's not a favorable quality for anyone living in a condominium built with metal wall studs. Anything solid that hits or moves against the wall can cause the structural material within to vibrate, and the sound will reverberate through metal studs, transmitting right into the condo next door if not also above and below. A University of California at Santa Cruz website notes that the most effective opportunity to take care of sound issues is when you're building your condo, but it is possible to damp some sound even if you're well past the building stage.
Search along the wall for any cracks and seal them with caulking. Seal any visible seams, too. D.L. Adams Associates in Denver, Colorado, notes sound waves don’t always travel in a straight line across a wall; instead, they “flank,” which is when they take a more circuitous route through spaces and cracks. Sealing up any possible openings can reduce the sounds created by flanking. To seal the cracks most effectively, you may have to check the entire wall, including the connections to other walls and to the ceiling.
Seal up and add sealing gaskets to electrical outlets along any walls you share with other tenants. Look inside the outlet box in the wall and seal any gaps you notice in the box. Before you reattach the plate, put a gasket between the wall and the plate to stop sound from leaking around the plate. UCSC notes this gasket won’t do any good if the outlet is right across from an outlet in the condo next door; in that case you’ll have to either wire a new outlet and just seal the old one up.