First off, there are two things to keep in mind when going for time on each of the bosses. By and large--you don't have to kill every part of the boss as the introduction screen tends to indicate. Each boss has a "weak spot" of sorts and attacking it full force will lead to a hasty death. With the exception of Posioden, you do not have time to kill everything (with Posioden you have to kill everything except for the smaller turrets in the third section).
Secondly, for each of the bosses you should try to come in with Full Health or very close to it. Having Full Health basically helps you keep your Double Weapon Powerup longer. If you realize that you are low on Health and there are no Health Power ups coming, I recommend allowing yourself to die when you see a Weapon Powerup on the screen. This will allow you to regain your Double Weapon status and "replenish" your health while you are at it. (I know it sounds odd that I would recommend killing yourself but getting more ammo on target for more time brings the bosses down a lot faster).
Third, save your Missiles toward the end of the level so that you have a full compliment of 8. Try to use the Big Bombs to keep yourself from taking damage if absolutely necessary. I say this because the Big Bombs quickly loose their usefullness once you find that the boss can't hurt you in it's Dead Zone. Strangly enough they even seem to take more time than the damage that they deal out. For certain bosses like Bodan, you may not have time to fire any of your Big Bombs to reach the S Rating cutoff.
Forth, come into the boss fights with Double Weapons. Any of the Double Weapons will do, so use whatever you are comfortable with. Most players seem to prefer the Double Laser so definitely give them a shot. As far as my personal best times are concerned, I did best with the 6-Shot (two 4-Shot upgrades.) The Double Laser "felt" and "looked" like it was doing more damage but seemed to take longer on the bosses for some reason.
Fifth, choose a plane that works best for you. For most people it seems like the Mosquito is the way to go. It has the highest amount of Health--meaning that you will keep your Double Weapon longer (or may not die at all), and it has the highest amount of Power--meaning that your Main Weapon will do more damage. It is the slowest of the three planes but if you work the Dead Zones that I discuss in the next section, you won't have to dodge as much as you might imagine.
Ok so lets talk about the bosses.
Bodan. S Rating Cutoff: 0-13 seconds.
Strangely enough Bodan is the hardest boss to get an S Rating on. His S Rating cutoff is so tight that you really don't have time to do much of anything aside from hammer and if you hope to finish him off in 13 seconds. Ok so, lets talk about the Dead Zone that I mentioned earlier. Bodan's Dead Zone is towards his nose right above the large turret that fires the large indestructable heat seeking shells. If you fire while above this turret you'll notice that Bodan's fusalage lights up. This is his "weak spot" and is really the only spot that you have to "kill". The other sections do not have to be killed and quite frankly you really don't have time to do so.
As soon as you can control your ship again fly straight to the tip of the tail and start hammering on your main weapon. Once Bodan starts flashing (he seems to be invulnerable for a sec) double up with your thumb and hammer and until all of your Missiles are gone. If you position yourself correctly the missiles will heat seek straight to the center fusalage but will take out the two tail gunner turrets on the way. Taking out these turrets makes it a bit easier to dodge bullets later on.
Next just focus on hammering and strafe up and down to avoid the sets of 3 big yellow balls from the wing tips. If you can avoid dying you should hit your time with several seconds to spare. Once he dies, you can crash into the nose of Epsilon if you want to check your time. If you feel confident, proceed on with grabbing the medals but keep in mind this might be time consuming if you continue to miss your time by a second or two.
If you don't hit your time, restart the game. Fortunately this is the toughest boss so if you can nab the S Rating on Bodan (after restarting a couple times if need be) you should be good from there on out.
Dagmor. S Rating Cutoff: 0-26 seconds.
Alright so Dagmor's Dead Zone is basically right dead center of his main turret. From here you can hammer away on and for the most part not get hurt. The only thing that you'll have to watch out for is the little turrets that will fire inward at you. The time is tight but not nearly as tight as Bodan so feel free to fire 2-3 of your Big Bombs to take out the small turrets.
With the smaller turrets gone, there isn't much that is going to touch you here in the center. Hammer away on as usual. Once he starts flashing double up on and until your Missiles are gone. Once they are used up continue in as usual. If you die--it's not a huge issue (if you are on Penguin you'll have plenty of lives so don't panic). If you die grab your Weapon Powerup, double up on and again and by now he should be pretty much finished.
Poseidon. S Rating Cuttoff: 0-1 minute 11 seconds.
Poseidon is a little bit different than the rest of the bosses because you have to kill just about everything. (I say just about everything because the boss won't advance unless the first two sections are completely dead. You can skip the mini turrets in section three however). There are still 2 Dead Zones but -just- hanging out in them (as you did with the other bosses) isn't going to completely finish him off.
The first section is a series of two smaller turrets and two larger turrets. I basically start on one side and work my way to the other (usually right to left). I'll throw in a few Missiles to speed it up but try to save at least 4 of them for section two. There is a mini Dead Zone of sorts above the larger turrets here, but watch the other turret if you are hanging out above one of these, it may swing around and shoot you.
Section two is basically two small turrets, two rocket launchers, and a turret on the bridge of the ship. Use up the rest of your Missiles here and try and knock out the little turrets quickly. The rocket launchers aren't that big of a threat so knock them out next and then proceed to the turret on the bridge. Right above this turret is the first Dead Zone. If you sit right above it, you can hammer away on and the turret (for the most part) shouldn't really hit you. This is one Dead Zone where Double Lasers seems to hit more of the weakspot than the other weapons. If you are using the other weapons (I personally use the 6-Shot) you are going to need to slide down a hair farther to get bullets on target. Hopefully Poseidon still won't be able to reach you.
Section three is basically one really big turret and four smaller turrets. Since you have quite a bit more time here, fire off any Big Bombs if you got them to finish off the smaller turrets. If you don't finish off the smaller turrets, its not a huge issue, once you make it to this section, Poseidon will die even if you just focus on the main turret.
Once some or all of the mini turrets are dead (if you choose to kill them), proceed to the next Dead Zone--right above the mini turret on top of the really big turret. The really big turret obviously can't hit you here, the smaller one will pepper you from time to time depending on the movement of the ship but if you adjust accordingly you should be able to sit right above this turret without taking much damage. If you manage your resources well this should be an easy S Rating boss.
Dagmor Sigma. S Rating Cutoff 0-1 minute 2 seconds.
Dagmor Sigma is really almost identical to Dagmor in terms of strategy. Fly right to the Dead Zone above the turret Hammer until it flashes and double up on and . Sigma has a couple more stages (rockets, fire, bullet rain etc.) so don't give up if he seems to take longer that his predecessor. You may die here but it's ok. Grab your Powerup and proceed in as before. If you can maintain your Double Weapon long enough you should be able to finish him off well within the cutoff range.
Bodan Epsilon. 0-1 minute 5 seconds.
I'm kind of embarrassed to say it but Bodan Epsilon probably has the biggest Dead Zone of all the bosses. His Dead Zone is similar to Bodan's in that it is right between the three turrets on his nose. If you position the nose of your plane right at the tip of the barrel on the center turret, much of Epsilon's attacks won't be able to hit you. This center turret will fire, but it will fire at a later stage so keep that in mind. If it does fire you can position yourself a little farther towards Epsilon's nose to avoid taking damage.
The strategy is the same, hammer until he flashes and double up on and . The only thing that you are going to want to do different here is "ride the crease" between the weak spot in the center of the fusalage and the two turret side panels on either side. It is possible to beat him with just riding the center but he seems to fall faster if you ride the crease and take out the two side panels while also damaging the center section. Most of Epsilon's attacks won't be able to reach you and as I mentioned previously you will never look at any of these bosses the same again.