This achievement is for playing as idol number 3, Hagiwara Yukiho, 5 times. You can choose for her to sing either solo, in a duo or trio and it will still count.
You can select any 5 songs for the achievement and at any difficulty. So, if you like, rather than playing through 5 songs fully, you can set the difficulty to hard and lose on purpose by depleting the cheer gauge by hitting notes deliberately off key. The menu that pops up when you lose asks if you want to replay from the start, say No (the right option), then it asks if you want to save (up to you, select either, left is Yes, right is No). In the next menu the first option asks if you want to replay the song again, this time select the first option. This will count towards your 5 song playthroughs too as well as.