I've only ever got past the drone stage once on normal. I've probably been doing something terribly wrong all this time, never looked at strategy guides or anything. Maybe I should try easy.
You should indeed. Focus on finishing it on Easy first.
If you need help/guidance, I made a couple of posts that might be useful:
http://www.neogaf.com/forum/showpost.php?p=45775649&postcount=1191
http://www.neogaf.com/forum/showpost.php?p=45834724&postcount=1221
There's also a new patch also.
Might be because FTL is apparently getting these new "Steam trading cards"; I just signed up for the trading card beta upon hearing of this.
Edit: Actually, there seems to have been a patch on May 30th:
Change Log v. 1.03.3
Tuning:
-You can now retrieve crew from a room when teleporting even if they are shooting at a door or walking, limit of 4 per teleport
-If you're carrying the Crystal alien from the stasis pod, the Rock Homeworld map will start with the appropriate quest marker to for the beacon that leads to the Crystal sector
-The Crystal Lockdown bomb is now available as a drop (from enemies or in Stores) in Rock sectors
-Shield Skill will level up when the shields absorb a hit, not when they recharge. This prevents turning the shields on/off to level up.
Major Bugs:
-Fixed: Bug that would sometimes cause an enemy ship not to get hit by asteroids in an asteroid field
-Fixed: Bug gave double rewards after victory when player teleporter was broken and crew 'used the shuttle'
-Jumping will now immediately provide invulnerability to solar flares, incoming boarding drones, and beams
-Can no longer open the ship upgrades screen in hostile situations using the hot key
-If the boss is destroyed, at that point game over will be blocked and your victory is assured even if your ship is exploding.
-Blast Door health will properly regenerate on safe (no current boarders) jumps
-Boarding Drones will no longer be hit by projectiles after they've successfully landed
-Boarding Drones will no longer be destroyed upon Boss Ship Super Shield regeneration
-Waiting in a nebula will no longer remove the sensor dampening effect
-Fixed: Sometimes enemy boarders wouldn't pursue any targets and just stand around.
Minor Bugs:
-Drones should no longer fly "into" the shields and fire past them.
-Dying crewmembers will stay dead if you Save & Quit + Continue. They will also remain unselectable and unmovable as soon as dying animation starts.
-Will no longer open the store / allow repair in the rare situation that you have 0 hull and should be dead
-Credits + Victory screen won't close if you accidentally tap a key - only escape will close it
-Missiles/lasers/asteroids/etc. will no longer collide with bombs since they are technically 'interior' objects
-The event where your crewmember goes crazy will have the correct race/name after going crazy
-You won't be able to waste your money choosing pointless repair choices at the repair station event
-Beam Weapons can now correctly cause breaches, but that will not come standard to current weapons to preserve balance so it's just for modders.
-Interior console glow fixed to display correct colors for crew levels
-Combat/Defense drones will properly trigger blue event options
-Drone / missile counts can no longer go negative
-Modding to have more than 4 shield bars will no longer make asteroids ridiculously terrifying
-Crew will no longer continue repairing a breach if the room is on fire, the fire will take the correct priority (as the animation shows)
-More grammar/typo fixes and minor animation/image polish