The Apollo Lens is effectively a large cannon. Built high atop the mountains of Angara, it operates by magnifying and concentrating light. It is described as the most powerful weapon of the ancient world.
Built in the ancient past, this machine is powered by the Alchemy Forge and Alchemy Well, and was part of the quest of the ancient world's quest to obtain power beyond their already-formidable mastery of the four elements, a quest Kraden describes as nothing short of seeking omnipotence. This power lead to at least two devices being constructed, the Eclipse Tower and the Apollo Lens, which revolved around Dark and Light, respectively. The Apollo Lens was built by the Exathi, however, due to the extremely harsh light that continuously bombards Apollo Sanctum, they had to be guarded though the use of the Umbra Gear in order to work. This was made by the Jenei, but can only be used by the Exathi, and was evidence of their strong mutual co-operation.
This device becomes known to the Tuaparang, who seek to reactivate it and claim it for themselves. They ally with Arcanus, a powerful Adept who gains their leader's approval, so that they may reach this goal. However, rather than actually set things in motion themselves, they manipulate Matthew's group into doing it for them. They start this by forcing them into Ei-Jei, from which the only way north (Matthew's group's actual destination), is to reactivate the Alchemy Forge and Alchemy Well in order to travel to Craggy Peak via Passaj. This serves to power-up the Apollo Lens. Next, after approaching the Mountain Roc to obtain one of its feather, they trick Matthew's group (or, more specifically, Ryu Kou, who was travelling with them at the time) into taking the Magma Orb from the Mountain Roc's interior and using it to power-up the Alchemy Dynamo. They do this by holding Eoleo and Hou Ju hostage within Belinsk Castle (as Belinsk's leader, Volechek, was tricked into believing that the Dynamo was a weapon that could give him enough power to oppose the nearby countries of Bilibin and Sana), with the only mode of entry through Belinsk Ruins, wherein lies the Dynamo.
The Dynamo is activated by Ryu Kou, and immediately triggers the Grave Eclipse. This too, was part of the plan, as it forces Matthew's group, desperate to stop the Eclipse, to unlock the seals on the Apollo Lens, a weapon which, if fired, would instantly halt the Alchemy Dynamo. But immediately prior to Matthew's group firing the Lens, the Tuaparang intervene, sending in their "soldiers" and Blados and Chalis. The latter are set upon by Arcanus, now known to be Alex, the mastermind behind the Golden Sun event, who betrays Tuaparang (though his motives are unclear). Matthew's party is confronted by the Chaos Hound, who is reluctant to fight them (or specifically, Sveta), but is nonetheless forced to when he is imbued by Darkness from Chalis and Blados (what happens to Alex at this stage is unclear, though it is at least certain that he is not killed). After being beaten, the Darkness either overflows or a fusion is triggered (depending on whether Blados and Chalis or the Chaos Hound is defeated in-battle), either way combining the three together into the Chaos Chimera. When defeated, it is revealed that the Chaos Hound was actually Volechek, but nonetheless, they do not have time to grieve, and Matthew attempts to fire the Lens. He is continually knocked back, unable to pass through the light bombarding the firing apparatus, and eventually Sveta resolves to combine her Umbra Gear with Matthew's spirit and fire the Lens, though it would probably lead to both of their demise. Seeing his sister in peril snaps Volechek back to his senses, and he halts Sveta's advance, before firing the Lens himself, ending the Grave Eclipse, but losing his own life in the process.
This has a noteworthy after-effect on the citizens still in Belinsk. All the beastmen in the city turn blonde and some even gain special powers (as one puts it, he can use "light" as opposed to the usual elemental abilities wielded by Adepts), though the game ends without further elaboration.
It is unclear what happens to the Lens after it is fired, though in game dialogue with the elders of Passaj does seem to indicate that the Apollo Lens can only be used during the Grave Eclipse. If true, this would explain why it was necessary to cause the eclipse, why the Tuaparang tried to prevent Matthew from ending it, and why there's no concern of the Lens being misused afterwards.