This achievement is pretty simple to achieve, there is a boss every 2 stages and the Tapesmith is found on 2 stages, which is on Stage 2 and Stage 9. The first boss you will encounter is Skullmageddon, which is on Stage 2 and he will drop 3 pieces of Mithril once you defeat him. Once you've got the Mithril, replay Stage 2 and advance through the stage past the Rooftops, enter the Tapesmith and upgrade any song for 2 pieces of Mithril, easy.
Also while you're on Stage 2 (before killing Skullmageddon) kick the trash can where the Baseball Bat and the Whip is, it will reveal a Hair Comb, pick it up and wait for the fight to start, get into a position where you can actually hit him with it, once you've thrown it and directly hit him, you'll also bag the 'Bone to Pick' achievement.
Good luck with the rest of the achievements.