Hmm, Shoot The Core type bosses eh? Well I have a few more ideas for bosses in this. Also I am getting a ton of Star Fox vibes from this now, mainly from the very nature of this game.
Here's some more bosses you should consider
-An organism-type boss. As seen before, it is possible to make organic-looking bosses in Fraxy, even without partsgraphics. I suggest there should be at least one in Project G, maybe that one being like a biologic weapon of the enemy or something. I'd suggest maybe an insectoid-type being.
-A dual boss. Make there one boss where there are two being fought at the same time. Perhaps the second one would reiodically support the first one, or the other one becomes stronger when its ally is destroyed. You can make them two of the smae type of fighter, or perhaps two totally different ships.
-A boss with a large weak point surrounded by large invulnerable plates covering it. The boss periodically opens and closes the plates showing its weak point in battle. This type of thing has been done with Fraxy bosses such as Ebo's Dobkeratops, and my Ultra Gemerl, but I think this kind might be good for Project G.
One variation I'd suggest of this (and one that would be a bit more realistic) is one where the boss has a massive wave motion cannon or something, but has to open up the plates and expose the weak point in order to use it. That would make the player have to damage it during the time when its charging up the cannon, adding challenge to it.
-A boss with multiple weak points. Maybe make there like a number of small nodes or something like that which have to be destroyed or something, and not just one spot. Perhaps instead, you can make it so that it has one big weak spot that is covered up, and it only reveals it after the smaller weak points are finished. This can easily be accomplished in Fraxy through variables or something like that.
-A boss with regenerationg weapons. Like it has multiple weapons that can be destroyed, but they return after a few seconds. I got this idea from Rolling Core in Gradius, and a ton of bosses in G-Darius. I figure this might make it interesting, as for its means of offense don't stay down, but destroying them will give the player a bit of "hang time" to fight it. Of course, the main weak point of the boss doesn't regenerate, and destroying that will finish it off permanently. I feel this would do very well in Project G, considering the nature of the Shriekers.
One variation I had on this type would be like a regenerating weapons boss fused with a multi-weak point boss. The boss would have a number of weapons that have to be destroyed first, and it keeps its vulnerable spot closed up. After all of them are destroyed, it enters a "recovery mode." In recoverey mode, it stops moving, reveals its weak point, and then fires a static attack for a few seconds, which is the player's chance to strike. After a few seconds of Recovery mode, all the weapons regenerate instantly and it closes up the weak spot again. The player would have to repeat this process until it falls.
-A boss similar to the Aparoid Infected Pigma boss of Star Fox Assault. This was my fav Star Fox Assault Boss by far, and if you could make something similar to this in Fraxy, I think that would be neat. Basically the boss has like a number of large, cannon-tipped claws, that also lunge at you at times. You have to destroy all the claws in order to move on to the second phase. It's sorta another multi-weak point boss, though different.
Video of the Infected Pigma boss for reference:
-A Battleship Raid-type boss. TV Tropes call this sort of boss fight a "Battleship Raid." Essentially it is a massive warship or something that is too big to be seen entirely on screen. Something similar to the Egg Carrier in Sonic, the Battleship Halberd in Kirby Superstar, my Neuroi Dreadnaught boss, Saggitarius in RefleX, and others. It has to be fought in sections leading up to its engine or command bridge or something, having the player slow work himself up and destroy all the turrets and weapons on it along the way. Perhaps with Try editing, this could be made easier, if you can.
Also I had an idea for the stages themselves. Are you planning on for the actual levels, making there any physical hazards in the level? Something the player has to manuver carefully around. It can be things like a maze of solid walls, large lasers that turn on and off periodically, the classic meteor shower hazard, conveyor belts that move the walls across slowly, or something like that. I'd love to see some physical hazards in some of the actual levels of Project G.