Monsters attacking the Artifact

You have very little control over it, it's mostly the RNG.

You can get it from...

• Opening doors
  Every time you open a door there's a chance of dust dropping, which is a random amount, I think I've seen numbers from 2 to 9. The hero Max has a skill which raises the amount gained if he is the one to open the door when dust is found in a room, he gets this at level 5 according to the wiki, and it's also available on the "third eye" item.
• Kill Monsters
  I believe every time you kill a monsters there's a chance they'll drop one dust, however it might be more complicated than that. The heros Golgy and Sara have a skill which increases the likely hood of dust dropping from monsters, it looks like it only applies to monsters they kill, they get it at level 3 and 7 according to the wiki.
• Selling items
  Some merchants use dust as currency to buy and sell. If you have items you don't need, and don't expect to need, you could sell them for dust.
• Modules
  There's a Major Module called the Shop which allows you to store a Merchant, which can build Dust if it's operated while there's a Merchant in it.
• Events
  There's at least one event/tower thing where you can pay industry for the possibility of dust.

Note that dust is reset after each level, as are certain excess items, while industry is persistent, (but more dust might let you get more industry, or food, or science) which effects whether or when selling items or spending industry is worth it.

As I said, I haven't played the release version much yet, there's likely to be more specific items and modules, but that's everything I'm aware of.

Regarding tactics/strategy, it's more about adapting your controlled area/which doors you open/build things on to make use of the dust that you have, as opposed to taking specific actions that grant you more dust, since often those actions simply aren't available.

Um...

• After you grab the crystal, the game spawns mobs endlessly (UNLESS you've managed to gather enough dust to power EVERY room then NOTHING ever spawns!).
• Endless points early game where it doesn't spawn the "module killer" crystals and you setup your dungeon with enough turrets. (Points don't really matter but why not? My current run is an Easy Science Pod on floor 6 with 22,000 points. On floor 5 I killed 12,000 monsters just for funsies lol.) You can get away with this even on "Module Killer" floors if you have enough repair, though it's much riskier and requires a lot more attention, of course.
• Most importantly: Endless Food if you can manage the above scenario while also utilizing a character who gets +0.2 Food Per Kill (Soylent Green). Yes that's right get your free, endless food today!
• In addition to food you'll really be min-maxing with free, Endless Industry if you also utilize Recycling in your farming setup. :D
• Since monsters only drop dust if you are lucky and have a Merchant who uses dust for currency you can clear them out of items! This is good to do even if you have full loot on all your characters because you can then sell the extra loot to the merchant on the next floor for bonus materials/dust. :)
• Oh yeah almost forgot there is an Achievement (I play on Xbox One) for surviving IN the exit/elevator for 1 minute. ;)

My current team for this is: Gork (Solyent Green at Level 3), Skroig (SG at Level 3 and SG2 at Level 11), Nanor (SG at Level 7), and Opbot (Recycling at Level 5 and Recycling 2 at Level 12). In the farming room (ideally 5-7 small modules with 2-4 Autodoc, 1 Defense, 1 Tear Gas, 1 Attack) I give Nanor the crystal in floors that need repair, otherwise I have Opbot hold the crystal so every single kill nets food and industry.

Doing this I can achieve hundreds of industry and food each floor. Though some floors just don't work...you absolutely need a single hallway leading from your farming room to your exit, with no monsters spawning on that "side" of your farming room.

Just make sure to have a good exit strategy to get everyone out of the room when you need to, like saving Skroig's Red Plume skill to distract all the enemies at once. :)

Edit: Took a screenshot for y'all. You can see I'm on Floor 9 (on an Easy Armory Pod run) with way more industry than I'll ever be able to use (I still had over 1.5k at the completion of this run despite filling pretty much every room I could with stuff), and my heroes are already way stronger than they should be ehehe. :)

Also I used an additional defense minor module instead of an attack minor module because I was able to fill a number of other rooms with Tactical Huds.