The Steam trading cards associated with it have descriptions for the bosses--in Japanese, at least. I got the Terant (boss 6) card at least when I first ran the game, and feeding the text to Google Translate spoke of it being constructed from a lost technology associated in some way with an underwater city (the verb in the translation was "chased"; I'm pretty sure that's not accurate).
So someone in the backstory may have forgotten that Atlantis was the villain in Platon's dialogues. -.-
Anyway, using the Community market, I'm ferreting out the descriptions...
TRANSPORT IMITATION (boss 1): 高高度よりメタンハイドレート輸送船を捜索しMH.PIRATE等の海上部隊と連携する空中指揮所。/An aerial command post that searches for methane hydrate transport ships from high altitudes and coordinates with maritime units such as MH.PIRATE.
WILD TANK (boss 2, rendered as "Tank the Wild's"): 大型車輪による走破性を活かした先遣強襲兵器。/An advanced assault weapon that takes advantage of the ability to run over large wheels. (I presume that's as in run over other tanks with its wheels.)
RAY (boss 3a): メタンハイドレート採掘エリアの輸送路を防衛するエイ型兵器。外装ユニットに応じ地上兵器にも空中兵器にもなる。/A stingray-type weapon that defends the transportation route in the methane hydrate mining area. Depending on the exterior unit, it can be a ground weapon or an air weapon. (Okay, what's all this about methane hydrate? {checks Wikipedia} So it's a font of natural gas you usually find underwater. Maybe this explains the relevance of the apparent Atlantis stand-in.)
MOVING FORTRESS (boss 3b): TANK THE WILD'Sにより制圧されたエリアを拠点化する移動要塞。/A mobile fortress that bases the area conquered by TANK THE WILD'S. (I think this means that it holds dominion in places the Wild Tank has already suppressed. How fortunate that you've already stopped that...)
MH. PIRATE (boss 4; I think we can safely say by now that it stands for Methane Hydrate Pirate): メタンハイドレート輸送船を襲う神出鬼没の海洋兵器。/A mysterious marine weapon that attacks a methane hydrate transport ship. (So Transport Imitation sights where hydrate is being sent, and the Pirate destroys the vessel while swiping the hydrate for Atlantis?)
GREAT TWIN BLADE (boss 5a): 山間部防衛用大型ツインブレードヘリ/Large twin-blade helicopter for mountain defense.
STEEL ELEPHANT (boss 5b): 極寒地でのメタンハイドレート拠点を防衛するためにアルキメディアン・スクリューを採用した輸送船から改装された極寒地用兵器。/Arctic weapon converted from a transport ship equipped with an Archimedian screw to defend methane hydrate bases in arctic regions. (I think this means the vessel that became the Steel Elephant was originally meant to be able to defend hydrate extraction, but Atlantis hijacked it and repurposed it to offense.)
TERANT (boss 6; probably supposed to be short for Tera-Tyrant): 海底都市に追われた文明の残した失われたテクノロジーにより製造された伝説の巨大飛行兵器。/A legendary gigantic flying weapon manufactured with lost technology left behind by a civilization chased by an undersea city. (Maybe the "chased" is "conquered"? As in Atlantis didn't develop the technology, but swiped it from someone else long ago?)
9TH LOST (boss 7): 海底都市に追われた文明の残した失われたテクノロジーにより製造された謎の兵器。/A mysterious weapon manufactured with lost technology left behind by a civilization chased by an undersea city. (I know, not much difference from Terant's description. I wonder if the Lost AI--I think that's what the green orb that shatters is--was stealing methane hydrate in part to reconstruct Atlantis through the Airdome?)
EDIT: 追 means to chase or to drive away, well enough. But I'm thinking the point is that the lost civilization in question was at one point in the far past driven into undersea cities. So...are we talking high-tech Deep Ones? Also, considering that the game was originally called G-Stream: G2020 and published in 2002, I'm wondering if the backstory/framing device (if ever we can find it) was that global warming in the year 2020 was thawing out arctic methane deposits. So of course corporates decided to harvest the stuff, turning it into the more solid methane hydrate for easier shipping. (Make the climate situation yet worse, why don't you...) Only to find that somebody else was attacking convoys and harvesting hydrate themselves. After attempts to point fingers at each other (the aggressors harvesting their own methane didn't exactly imply monkeywrenching), the corporates finally figured out that the "pirates" were actually some odd military force beholding to no one, necessitating that the world's militaries cobble together G-Stream class fighter-bombers to repel this mysterious force (the delta in DeltaZeal probably is meant to signify change, as in your weapons system). Ultimately, the villain turns out to be an AI-assisted undersea megapolis/airdome whose inhabitants were happily taking advantage of the warming planet to refuel their engines of conquest. (This sounds a touch like the Gorn in Blast Wind, actually, swapping out nuclear exchange for global warming. So this definitely isn't a new thing I've cobbled together...)
EDIT THE SECOND: Transport Imitation is probably supposed to be Transport Pursuit. 後追い can apparently translate to both pursuit and mimicry...