The last achievement of the game, with the toughest challenges. Here are the challenges:
1) Promoted to Major General (previous rank)
2) Clean game time is over 24 hours
3) Encounter the killer piano
4) Finish a stage with half or less second remaining
5) Complete arcade with all pilots
6) Arcade 1CC (Complete arcade without using a continue)
7) Complete arcade using only your primary weapon
8) Finish a stage on insane without picking up anything
3) The killer piano is a random item dropped by enemies. It's blue and has more of an obvious colored aura around it than other pick-ups do, and the icon is white piano keys. As far as anyone knows, the drop is completely random and can show up at any time in any mode. It's a joke item that summons a piano that instakills you. One thing to note with the piano is that it seems to have "stuborness" coded into it - during my first 20 hours with this game, I saw the piano twice. Then, in the following hour of gameplay, I saw it almost a dozen times. I think that happened because I kept managing to dodge it and the game insisted on spawning it until the piano finally got me. After it did, I haven't seen it again in the following 2-3 hours of play. So if you see the piano icon, just grab it, take the death and avoid the piano trying to haunt you for hours.
4) The easiest way I found of beating a level with 0.5s remaining was Boss Training against Kolobok. I removed the cannon on top and all of his tentacles, so all he has left are easy to dodge missiles and the laser. Then I took his life bar down to basically nothing and waited for 0.5s, then took the final shot. I didn't need to count seconds or anything - the timer in the game is so large and clearly visible that you can see when it passes 0.5s and then press the fire button.
5) Complete arcade with all pilots is going to be tough, considering about half of the pilots just plain suck. You should probably save this one until after you can complete challenge 7, as that will give you a lot of practice with not relying on your subweapon. The Sonic Sword, Azimuth Battery, Gemini Drone and Seeker Missiles certainly aren't going to help you kill bosses very well.
6) Actually not the toughest challenge in the game (that's #7), but still challenging. All I can say is that you need to practice, and use all of the game's tools to your disposal. Unlike most shmups, Sine Mora gives you a lot of handicaps. You can have both a time extend and a shield at pretty much all times, and any troublesome bullet pattern can be negated by using your capsule. I suggest using the Liberator, either Lynthe Ytoo or Garai and the Reflection capsule for your Arcade 1CC. The Liberator has a good balance between damage and spread (unlike the Soprano) and the Reflection capsule is the best one - you can just use quick taps to hurry through a bullet pattern without using too much of your capsule. Lynthe Ytoo has the best overall subweapon, but there's a good trick with using Garai - he can kill Domus, the hardest boss in my opinion, without even bothering with the red lasers at the end. Just fire his cluster bombs towards the core of the boss structure, through the walls, when you enter the red laser area and you win. Eventually, you'll have to master beating Domus manually if you want the full 200, but this is a great method for getting the 1CC out of the way and cutting some of the pressure.
7) This is another one you just have to practice and nail manually; no tricks available here. The only thing I can say is that it doesn't need to be done in one credit. Getting A ranks in Score Attack (for a previous achievement) is a fantastic way to practice, as you'll be doing mostly primary only when you're trying for high ratings and in Score Attack, you'll need to learn to master each level starting at weapon level 1, unlike a regular arcade run where you'll be entering each level with at least weapon level 3. Arcade will feel like a breeze if you master Score Attack first. One thing to keep in mind is what pilot to use for this, as you should be using whoever you feel has the worst subweapon. In my opinion, that's whoever has the Azimuth Battery as that one feels both weak and useless. Seeker missiles are pretty useless too. Definitely don't do it with Ytoo, Koss or Garai as those guys have subweapons that are great against bosses.
8) Straightforward challenge that can be pretty frustrating and hard. Don't bother trying the final boss even though that sounds tempting and easy; your level 1 weapon is too weak to kill the various parts of the boss before time runs out. Level 1 is probably the best for this, though I'm thinking the short and strangely easy level 5 might also work. Don't make the mistake I did at the end of a near-perfect attempt; if there are items 2-3 inches away from you when you enter a "time mass stabilized," those items get sucked to you and ruin your attempt. Stay far away from all items when you know a "time mass stabilized" checkpoint is coming up. Pesky, annoying challenge that's counter-intuitive and unfun, but at least it's short and not that hard.