You can access radio conversations by using the
button on your controller. It's advised that you hold the
button to speed through your conversations. Each person may have more than one thing to say, so you're encouraged to talk to them more than once. The achievement will unlock after making all the calls.
I would recommend saving with Courtney after you finish your calls. It is unconfirmed whether or not restarting checkpoints voids out the calls, but it's probably not a smart thing to do. Codec conversations do carry over playthroughs so long as they're on the same save file. When should you check for new codecs? At the beginning of every level, after checkpoints, fighting enemies (especially new enemies), at the beginning of a boss battle, at different phases of a boss battle, after rescuing civilians, etc.