How can I get a Blaster Launcher?

Building the Blaster Launcher requires that you:

• Encounter and shoot down a "Battleship" class UFO - one spawned for me while I was in the process of building the Gollop Chamber. Anecdotal reports indicate that you can get this to happen prior to building the hyperwave relay. If you move fast through the campaign/story missions, you may never encounter one of these.
• Recover its Fusion Core - It's a bit of salvage you find when you complete the mission to scout the wreckage. If you get close to it during the mission, your chief engineer will remark about how it could be used to advance your weapons technology.
• Research "Blaster Launcher" technology - This is one of 2 research projects that is available after recovering the core. The core is not consumed in the process.
• Build a Blaster Launcher in the Engineering section of your base - once you've done the research, you can build the launcher. It replaces the rocket launcher as the secondary weapon for a heavy, but unlike the alien grenade, you must build one for every solider you wish to equip. Building the Blaster Launcher does consume a Fusion Core, in addition to other resources.

The Battleship can be difficult to shoot down, so send your best interceptor after it if you can, and be ready to use your boosts. The Battleship salvage run is also a large map - plan for an engagement that's just slightly shorter than assaulting the alien base. There's no mistaking this for one of the smaller craft, it's probably about double the size of the supply ship. Try to shoot it down with an EMP cannon, to maximize your chances of getting 2 Fusion Cores intact.

PROTIP: you can force a Battleship to appear by ignoring a UFO that is on a "scout target" mission - after a few days a Battleship will appear over the same country on a "destroy satellite" mission. This way you can farm Fusion Cores for Blaster Launchers.

Alternatively, if you have the Slingshot DLC, that series of missions culminates in disabling a battleship well before you'd normally encounter one, with two guaranteed intact fusion cores as well as a lot of Elerium and alloys.