Here is the full list of all 13 LinearShooter Remixed achievements.
Clear Stage 5 with Unknown.
Clear Stage 5 with Type-C.
Clear Stage 5 with Type-E.
Clear Stage 5 with Type-F.
Clear Stage 5 with Type-B.
Clear Stage 5 with Type-D.
Clear Stage 1.
Clear Stage 2.
Clear Stage 3.
Clear Stage 4.
Clear Stage 5.
Clear Hard mode.
Clear Stage 5 with Type-A.