There are 35 songs to play through in Duet Mode, and they can be done in any order. Only one USB Microphone is needed, as the game will still play in "Single Mic Duet" Mode.
Each and every song must play through entirely, but no score is required at all for them to count for the Achievement. The Achievement will unlock when the game saves following the 35th song.
I suggest muting the volume and enjoying a good book while the songs play out. At an average of, say, 4 minutes per song, you're looking at about 2.5 hours of Disney tunage.