This is the first achievement you will get.
YOu need to get a record on five different songs. Now don't confuse 'a record' with 'a high score'. You actually get a record (bronze, silver, gold etc.) for reaching a particular score in a song.
When you start up the game, you can only go for BRONZE records, which are awarded for getting 50K points in a song.
So, sing 5 different songs and reach the required score in each of them and you'll unlock the achievement.
If you aren't much of a singer, wait until you level up and unlock score multipliers.