I tested beam weapons vs the Guardian rather thoroughly. All the following used 210 weapon space, in Battleships with HEF, Hyper-X, Rangemaster, as well as Battle Pods, Aug Engines and Battle Scanner.
NOTE: I typically bring 6 ships, but I was Creative; the number of ships necessary may be greater than what I list below if you lack things like Megafluxers.
Or, say, if you can't beat Orion's 34 Initiative. I had 19 speed (Hyperdrives + Augmented Engines) + 165 or more Beam Offense (Positronic Comp + Battle Scanner + Regular or better Crew) = 35+. So skipping a computer because you have Maulers and think you don't need it may be a bad idea. It's not like they take up any ship space.
A Weaponry officer can also help with this due to increasing Beam Offense, and Navigator for speed.
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Briefly: If you have High Energy Focus,
Gauss Cannons are the cheapest option that does the job reliably. Unless you have a good Ordnance officer, then Phasors can do it too.
Less briefly:
(Every weapon had 1 level of refinement)
26 Phasors or 13 HM Phasors
vs Class X shield (10) and Hard Shields (3), 5-20 damage is harshly trimmed even after HEF.
No leader: My usual choice of 6 BBs failed horribly. Took the shield down, but that's all they did. Built 6 more, and even as 12 they couldn't really do much to the armor.
Adding a 22 Ordnance officer let 5 BBs do the job, though.
Then I tried 12 BBs with HM Phasors (and no officer), on the theory that HM will help beat the 13 points of shield absorption per shot. Funny thing happened. I fired my full round 1, then on the Guardian's round 1, it killed 3 of my ships, the third one exploded and the death explosion killed the Guardian.
26 Gauss Cannons
18 damage + HEF beats the shield rather nicely, AND they are more space-efficient than Phasors per damage point, AND they don't dissipate.
5-6 ships needed normally, 3-4 with 22 Ordnance.
10 Plasma Cannons or 5 HM Plasma cannons
No leader: 6 ships did even worse than Phasors, didn't bring down a shield. 12 did it, but barely. Took 2 rounds and lost half the fleet.
Of course, 22 Ordnance Makes Everything Better. 3 ships did the job with that.
Heavy Mount also helped, probably by reducing damage dissipation and by beating the shields by a larger margin. The Shield went down faster, and when I brought 12 ships, the 9th ship killed Orion on turn 1.
13 Disrupters
Pure awesomeness. This is the best weapon in the game, especially after you autofire it, if you are not facing Reflection Fields and if your your Beam Offense isn't horrid (in either of those cases, go Maulers). My general-pupose ships always get a few heavy mount, too, to kill planetary defenses behind Barrier Shields. (I only take them against Antarans if I have Damper Field, and then I still go fully Heavy Mount. But I digress).
Anyway, we're sticking to 1 refinement here so no autofire or other gimmicks:
3 ships normally, 2 with 22 Ordnance.
4 NR Maulers
Are space-inefficient compared to Disruptors, especially once you can autofire them (*), but they're still a good choice for Guardian, if for some reason the Guardian is still in the game while you teched that high.
3 ships normally, 2 with 22 Ordnance.
(*) Maulers' only function in this game as far as I'm concerned is to beat Antarans, or anyone else who has Reflection fields, due to the Reflection Field failing more the more base damage you're doing. I suppose you can always use them to compensate for not having a computer, since they don't miss, but using beam ships and NOT having a good computer (initiative!) seems kinda insane to me.
Of course if you're going to tech as far as 1-refined Maulers, you may as well try...
19 HM AF Phasors
No leader: 5 BBs did it
22 Ordnance: Only 2.
Makes sense, assuming that Ordnance is a flat addition to damage per weapon, rather than a percentage as strategywiki says.
EDIT:
But I think it would be cool to find the new MINIMUM fleet required to take this bad boy down.
Cool story, and with 7BB's you have set the new minimum fleet record
Haha. Well my record was 2 BBs until I read this.
Then I researched Physics 1, to get...
13 AF Disrupters (With the 22 Ordnance officer)
1 BB killed the Guardian. Total 14 Disrupters fired (Hyper X). The first salvo cleared the shields, armor, structure, and slightly ate into the engines. Save attached.
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Is it too difficult to kill the Guardian now? HELL NO. Keep it like this. Please. Same with Antarans.
In fact, consider taking out the Automatic Repair (unless it's necessary to repair after surviving a battle?), and putting in something to make it able to take more damage. Energy absorber would be a good pick, or Displacement Device.
Or maybe Heavy Armor? I forget if that can be circumvented with beams, without late game tech. If I understand correctly, Heavy Armor would make it harder for beams but not affect the EMG missile strategy. That would be a good thing.
(Probably not Reflection Field, and not Phasing Cloak, not when Orion is supposed to be conquerable early enough to make the techs from it useful).