(See also Kawaiikochans on this game.)
Galaxy Force II is a game that requires extremely clean and precise play to finish without continuing: at first I thought the game was just designed to need a continue in order to get to the end.
But it's possible! The achievement took many hours of on-and-off play, mostly a playthrough or two every time I was on the subway for a long trip. Yesterday I came back to the game after a few weeks off it, and sure enough I got my perfect run. Enough of that, though, I want to do a strategy post.
(This post will refer to “stage 1” and so on assuming you start at Megaleon, the default first stage; starting on other stages changes the level design and difficulty somewhat.)
THE ENERGY METER, AND “GOTTA GO FAST”
The energy meter is both your life meter and your time limit. It starts at 1200 and is constantly ticking down, and fast. As such, it makes sense to fly through the stages as quickly as possible. You should have the throttle at maximum for most of the game: aside from turns, braking is rarely necessary and obstacles shouldn't be too difficult to dodge at full throttle.
THE ENERGY BONUS AND “GOTTA BLOW UP EVERYTHING”
If you stop there and just race through the game avoiding all damage and enemies, you'll run out of energy and lose anyway. Not only do you have to run the game at top speed, you need to be shooting down nearly everything you see. You're given an enemy bonus for enemies shot down which is usually refilled at the midpoint of the stage, and this bonus is the only thing that's keeping you alive from stage to stage.
If you are not over 1000 energy by the final stage, you will not be able to finish the game. To be at 1000 by that point, you have to have done an excellent damn job.
MISSILE AND GUN
If you move to the area an enemy formation is in and hold still for a moment your missiles should lock on to all of them. If you don't keep steady you won't get a proper lock on and probably miss a lot of valuable hits.
Since neither missile nor gun expend energy you might as well be firing the gun at all times. Missiles do most of the work, but the guns shouldn't be neglected. You'll need them for close targets, times you're between missile volleys, and especially the big, slow targets with lots of HP.
KNOWING WHAT TO BLOW UP
Most things should be blown up. Some things must be blown up, and others are kind of wasteful and pointless to blow up.
Must: Obviously the other fighter planes. A formation of these guys will get you a lot of energy and you can't afford to let many of them pass. Move from formation to formation and take down as many as you can. Go where there are lots of them and don't waste time chasing a straggler if there's a whole formation coming up.
Should: The big targets. The ship in stage 1 (no excuse not to get this one), the lava snakes in stage 2, and other similar targets you'll see in the other stages. The lava snakes are the biggest energy point boost I know of and if you know where they are it's a breeze to take most of them out. The hopping robots in stage 4 don't seem like major targets, but they are.
Doesn't really matter, is kind of in the way: Debris. There's a lot of debris in this game thrown in to kind of throw you off the enemies you should actually be shooting down. In a lot of cases you might as well just shoot them (pollen in stage 3) but you're making 1 point per object so it doesn't really matter. In other cases your missiles will lock on to the debris when you want to take down the fighter plane that's flying among it, so you're forced to go to the gun.
There's a lot of case-by-case stuff where some background targets are worth a lot of points (the garages in stage 4), and others aren't worth jack (garage, stage 1), and you just have to feel them out case by case-by-case.
The blue bits on the floor in stage 3 look like debris but they're worth a lot of points. I didn't figure this out for the longest.
Speaking of knowing when things is going to happen, Galaxy Force II punishes the player who tries to play memorization style. You can't run to the place where you think an enemy is going to spawn, because the enemies will always spawn at a certain distance relative to you. You can know where the enemies are showing up, but you cannot attempt to meet them in advance. You have to know, then see the enemy come, and finally react to them.
It's the same with the nasty, huge obstacles in stages 3 and 4: let them appear and immediately move the hell out of their range without neglecting to shoot down what you can. Don't try to get around them early, they're programmed to pop up in your face and force you to deal with them. Assuming you start at 1 (Megaleon), 3 and 4 are probably the most annoying stages.
Anyway, you're on your own from there, best of luck. It's very doable, and there is wiggle room if you get hit a couple times, just not a lot. Here is a one-credit play video from the PS2 version that helped me a bit with some of the finer points.