There are several ways in which an apartment tenant can deal with barking dogs. First and foremost, have a conversation with the person who owns the dogs. Explain to them your frustration and ask that they ensure their dogs do not continue to bark. If that fails, place your landlord on notice. Explain to them, in writing, them problem and ask that your landlord speak to your fellow tenant about the problem. At the same time, don't hesitate to call your local police department on their non-emergency number about the noise the dogs are making. Dog barking can violate your local noise ordinance. At the very least, your calls to the police department will create a record you can show to your landlord. If you have a responsive landlord, he or she will ask the tenant to leave or take steps to evict the tenant. If you landlord does not take steps to evict or otherwise remove the tenant, consider telling your landlord, in writing, your desire to place your rental payment in escrow until the issue is taken care of. Finally, if this still does not stop the barking, you can file a civil action against the fellow tenant and your landlord for nuisance. At this point, you ought to consider moving out as well, as a civil action can add additional weeks or months.
Disclaimer: This does not constitute legal advice. No attorney-client relationship has been formed through this answer.
Have you talked to the owner of the dogs? They may be unaware that their dogs are barking for that amount of time. If the owner is not responsive. keep a log of the dates, times, and duration of the barking and call animal control and/or the police.
If we do not have a signed fee agreement I am not your attorney and this is not legal advice.