Here is the full list of all 16 LEZ achievements.
Complete the tutorial (Welcome to LEZ)
Complete a song of 1 star or more
Complete a song of 2 stars or more
Complete your first song
Complete a song of 3 stars or more
Complete a song of 4 stars or more
Complete a song of 5 stars or more
Complete a song of 6 stars or more
Complete any map without fails
Get a maximum combo of 100
Get a maximum combo of 250
Get a maximum combo of 500
Get a maximum combo of 750
Complete a song of 7 stars or more
Complete a song of 8 stars or more