Report them to code enforcement.

Get loud about it. Start by telling them you'll contact all of the local news channels. If that doesn't work, then actually do it. Post anywhere you can online, and especially in local newspapers (print still carries more weight, most often, than something posted online, I have found), don't stop until they fix this.

Two winters ago, my son had a rat infestation (not their fault). The rental company “didn’t believe it” and ignored it. Upon moving appliances, he found old holes filled with steel wool. Only after wires started smoking did the company half assedly have Orkin come in. It just got worse. He warned the company he would have to move. So in the middle of February we moved them out. They left three months before the lease ended. Code enforcement was called, but he did nothing even after sounding concerned. About a year later, they started demanding payment. Then sent the account to a lawyer. My son had pages of texts and documentation, pictures, and videos. He thought it was resolved. He was going through a mortgage process last month and bang. They had sent it to collections. Yes, he could have been more aggressive. But the result of this is moving in the middle of the winter and having his good credit messed up. Like someone said, make this public knowledge and fight like Hell.

If you are in a city with a health department go there. You can call 211 and see if they have any suggestions. For anything, 211 is a good resource. Tbh they get half their answers from Google but it's a free call.

Shout it from the rooftops! Every Avenue of social media. Withhold rent.

Start by sending them a registered letter through thenUS mail explaining the issue and indicating dates that you have attempted to contact them, ask them to fix them problem with in 2 weeks. Follow up with a second letter if they have not and meet with your local code enforcement officer - bring a copy of the letter that you sent the landlord.

You'll want a lawyer before you do anything drastic. Reach out to Pine Tree Legal and ask for a consultation. IIRC they're free.

I do not know the laws around roach infestations, but as with many issues affecting the habitability of a unit, you might be able to pay for the fix yourself and deduct it from your rent.

Regardless of whatever decision you make, you will want to keep a written or digital record of your actions, experiences, and communications and you will probably want to begin to look for new housing. Landlords tend to not look kindly on tenants exercising their rights.

As others have said, report to code enforcement but make sure you do it in writing and get confirmation. Pretty sure you can use that as a defense if he tries to evict you (retaliatory eviction) after that.

after you've done what other people in this thread have mentioned -- withhold your rent until it's resolved.

Your landlord needs to get rid of that do-nothing cockroach in the front office.