Oh man, I am right there with you. They would come into my apartment last year, and we aren't talking the little indoor ones - these were the HUGE ones you see on the sidewalk. Awful. Skin-crawling terrible, I tell you! I'm shuddering thinking about them right now. Below is my four-point plan of attack.
1) By law I believe your building is required to offer monthly fumigation. Be sure to tell your encargado that you want this fumigation scheduled and you want to know exactly when they are coming. Even though sometimes they come, the fumigator will often skip apartments and say he did the whole building. I used to stalk mine and I actually chased him down on the sidewalk once.
2) You can buy a gel that is quite effective in killing the little jerks. I don't remember what it's called but if you just walk into any hardware store and say 'necesito un jel (pronounced 'hell' more or less) para matar cucarachas' they'll get your drift. Put it near water sources or wherever you think they're coming in. They'll still appear in your apartment, but belly-up, which is a lot easier to get rid of.
3) Sweep often, clean your countertops, and don't leave any food out, ever. Also, try to keep your place as dry as possible as they need water to live - no standing water or dripping faucets.
4) Mine came at a rate of about 2-3 per week. If yours come much more frequently and nothing helps, it might be a lost cause and you should consider moving. If you try to address the problem via your encargado and after a month it still isn't resolved, you should be able to use that as a reasonable excuse to break a contract (but, as we've all read many times in this forum, 'reasonable' is not a common word among those in the real estate sector).
Best of luck!