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When you encounter the plague-infested station, if you have an advanced medbay and the Engi Med-Bot Dispersal augment, you can cure the entire station in less than a minute. Even the game notes that the colony leaders are astonished.
Having the appropriate weapons for the Giant Spiders: Gliding up to the airlock and letting an anti-personnel drone to quickly kill the creatures, or the more awesome (if less rewarded) option of slamming a boarding drone through the stations hull before it starts tearing the spiders apart, or the surgical option of using a bio-beam to pick them off one by one.
The Weapon Pre-Igniter plus a crazy-powerful weapon like the Glaive Beam.
If you're very, very lucky, you can get the Weapon Pre-Igniter as a post-battle reward, a surrender offer, or best of all, a random "found an item" event. This can happen in sector one. If that happens, have fun breaking the game.
For example, you can use the Pre-Igniter to defeat an enemy ship without letting it fire, or if the enemy is weak enough and your weapons are powerful enough, you can destroy it in a single Alpha Strike.
The first time you do the former situation will actually give you an achievement called "They never saw it coming".
Masterful use in the DA-SR 12 results in this, if you find a Pre-Ignitor alongside a Flak II (if you have Advanced Edition turned on of course). Even the mighty Rebel Flagship itself stands little chance aside from the occasional lucky shot in-between cloak cooldowns.
Sending more than one Boarding Drone is also hilarious: punching holes in the enemy hull and watching your killer robots rampage through the enemy ship is awesome.
Automated Loader + lots of burst lasers + upgraded weapon crew member = fun for the whole family. Also note that the reloader can stack and is quite cheap.
You may encounter a Mantis Cruiser lined with Rock body parts. If you're flying any of the three Rock Cruisers or have the Rock Plating augment, you get an option called "Ram the bastards." Doing this will disable the Mantis ship's engines permanently allowing you to get guaranteed hits, in a very rare opportunity to preemptively disable an enemy's systems instead of the other way around.
Outwitting the Slugs, whether it be by using your own Slug's psychic powers to sense their attempts to plunder your ship, letting a Rock crewmember No Sell a spiked drink, getting a Mantis to slice them in half after they try to lure you off your ship, or just by forcing them to surrender after kicking the crap out of their ship.
A big one for the developers; after delivering an absolutely fantastic product, they went on to tweak and improve it, fixed a bunch major bugs on the way, and slapped on some serious content additions, effectively creating what other companies would sell as sequel, or at least a major expansion pack. What does Subset Games do? Release it for free.
If you can send 4 Mantis onto an opposing ship using a Teleporter, they'll kill the entire crew, assuming there is any. Medbay? No problem, they'll kill the fleeing crewman before it can even leave the room. Clone Bay? Even less of an issue. And they can do all that without any fancy Crystal Lockdown power or even a simple hacking module latched onto the Medbay. Watching your Mantis systematically murder the entire crew of the Rebel Flagship like this is truly a sight to behold.