This achievement will unlock once you have sent 20 text messages through your cell phone. If you answer every possible text message, this should happen on Day 5, but the achievement will not unlock until the end of Day 8. There are 25 text messages you can reply to in any given playthrough.
Keep in mind you can almost always get another text message to respond to by replying to Catherine and Katherine in the way they prefer (Law for Katherine, Chaos for Catherine). Refer to the Phone Mail article for a list and guide of all text messages.