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