Ask him if he can pay you cash daily because you need it for food, then settle for weekly. Tell him you have another offer from another agency. Don't accept a pay delay, but expect one. Nail him down on the pay date, and when that day comes and he delays, tell him you need it for rent, can you get 1/2 of it? The day before pay is due confirm with him you will receive your payment.
Small businesses are like this all over the world, not just Peru. Forget about trying to work legally, you don't want to pay taxes anyway. Getting this paperwork done would take too long. Other choices could be working for a Hostal for free room and board.
..A Peruvian once asked me:what's the difference between special and abnormal?.....well my answer was : Lady Gaga and Miley Cyrus..