Your landlord likely has few defenses to your claim. In additon, California has a law, called the collateral source rule, that does not allow your landlord to deduct your insurance recovery from any damages she owes to you. Therefore, you should be able to recover your damages in court as long as you don't overexaggerate them. Take pictures, list your damages on one page and include receipts. Organize your presentation and go to court.
Your best bet to recover damages is in small claims court, not from the City.