Can I break my lease without having to pay for the remaining months?

Probably. You need to gain documentation. Send a certified letter to the management explaining the the entirety of your complaint (unfinished repairs, 2 burglaries). Recite the chronology of the complaints (give dates) and the numerous times you have requested their assistance to rectify the situation. Include pictures of all the repairs needed and police reports for the burglaries. Explain that if reasonable attempts at repair have not begun within 10 days you will be forced to give notice. After the 10 days give written notice and include a copy of the original complaint. If they fix things still give 30 days and move (if you want). Leave the place as clean as possible. Take pictures of the place before you leave it. You should only be liable for the time period the apartment remains unrented plus reasonable advertising, and really, it sounds to me like a judge might agree with you that your breach is justified if they haven't completed promised repairs (may depend on the extent of the repairs or the contract language or both). Anyway, if no one will rent the place due to the needed repairs then you shouldn't have to pay for that period either. Depending on how expensive your rent is it may be worth speaking with a competent local attorney.

I agree with the previous attorney's advice that you must give the management notice in writing of the issues that need to be resolved. Expect to be sued by the landlord even if you give notice, they will try to bully you into paying a settlement regardless of your rights. However I would also expect a judge to be sympathetic to a tenant whose apartment has been broken into twice while only living there for less than 3 months. Read the terms of your lease agreement and your rights under the TN Landlord and Tenant Act.