This achievement basically only contains cumulative challenges. There are no special tricks to collecting 1000 powerups, playing for 20 hours or reflecting 10000 bullets. Just keep playing normally and you'll do it. These are the challenges:
1) Promoted to Major (previous rank)
2) Pick up 1,000 power-ups
3) Clean game time is over 20 hours
4) Reflect 10,000 bullets
5) Play with 40 different chronomes
6) Finish every stage with an "A" (or better) rating
7) Complete arcade with 2 different pilots
8) Finish any stage on insane difficulty
4) If you don't use reflect very often and find yourself needing to boost the 10,000 reflections, an easy way to do it is to load up Kolobok in Boss Training and just wait for him to do his screen-filling attack. You have enough capsule to reflect his laser and other shots too. After reflecting, just hit pause and restart stage.
5) "Chronomes" are the builds available in any mode but story mode. After you pick your ship, pilot and capsule, you'll see a hex grid with numbers on them. These are the "chronomes," so it's just a weird word for build. It marks them with a different color when you've done them. You can pick a different chronome than the one you just made by hovering over a number and pressing X, which is nice for systematically getting them all done. You can use any mode but Story and you don't even need to finish a level; just load one up and quit out if you just need to grind through chronomes.
6) "Finish every stage with an "A" (or better) rating" sounds like the hardest achievement in the game until you notice that it's cumulative and does not need to be in one run. Since it's a score attack challenge, you can pick specific levels and practice each until you get it down. The game doesn't let you know which levels you've completed so far, so keep track of that. See Help & Options in the game for a good explanation on how to keep your rank up. It's not as hard as it sounds, and keep in mind that using a subweapon lowers your rank by A LOT less than using your capsule does. The laser subweapon shoots away bullets too, so it can basically act as a slow-down that doesn't completely ruin your rank.