Use the chrono goggles on the British doctor to speak to him. He is the person with the mask in the street just after leaving your courtyard.
Easy "Micro killers" achievement
Use the chrono goggles on the microscope in your house to start a mini-game featuring the bacteria responsible for the plague.
Easy "Path of the Plague" achievement
Use the chrono goggles on the computer in Arnetto's house to start the map mini-game.
Easy "Plague purging" achievement
Get the antibiotics from your parents' room using the chrono goggles. Use one on yourself to restore your health. Consider speaking with the sick characters or walking near the rats (before discovering that they can be eradicated).
Easy "Rats!" achievement
After getting the chrono googles, go to the market and select the rat poison. Use it on the first rat encountered.