FTL is a great game because it has so many variables to account for, and this is especially true for hard mode. I have personally finished hard with every ship in the game, but I noticed that there is a lot of information out there that I consider inaccurate. Instead of writing a long guide, I made a simple list of do's and don'ts for FTL. These should help you make the right decisions in the game.
Keep the flagship in mind throughout your run. Your goal is to build a ship that can take down the flagship, not just get to the last sector.
Try to fire first. Get your salvo off before they can fire on you, or board and destroy their weapons before they can harm you. Slow weapons are a problem.
Get several defensive options for different situations. Get some shields, but also evade or cloak, or a defense drone.
Go for crew kills, these net more xp and will let you snowball a run, they are also fun to do. If you have good boarders, get a teleporter.
Get hacking. Hacking is the most useful system along with teleporter, and can help you out in many situations or even achieve crew kills by hacking oxygen. You can bypass defense drones by depowering your hacking module at the moment the drone fires its shot, then immediately repowering after the shot passes.
Try to upgrade systems that go well together. Hacking and drone control don't go very well together because they consume the same resource (you usually want hacking), but hacking has good synergy with stealth. A zoltan shield goes well with evade and stealth, mind control goes well with bombs and teleporting. Achieve synergy.
Plan your path through the sector. Go for a snake-like winding path that lets you scout for shops. Maximize nodes and dive into the fleet on your last jump if you have strong engines, if that will net you another node.
If you see a shop, pass by as many nodes as you can before actually visiting the shop, to build up a stack of cash to spend on a good upgrade.
Get long ranged scanners.
Pass through nebula nodes, these slow down the fleet and let you rake in more cash.
Avoid natural hazards unless you're equipped to handle them (sometimes asteroid fields can make for easier fights). Avoid pulsars and ion storms.
Train your crew if you find yourself up against a ship that cannot harm you.
Upgrade your oxygen and med/clonebay at some point, these give you blue options and put you in a safer position and lower downtime.
Get a clone bay if you have the option to choose, since it is better during your run because you can risk more events without consequences. The giant alien spiders aren't dangerous if you have a clone bay, and the clone bay is also generally better for mass boarding. Medbay is fine but less good.
Try to get good weapons that make sense for your run. Some weapons are generally good, others suck but some are useful in niche situations. Bombs can be a sensible choice if you have mind control and boarders.
Know which sectors to choose. Pirate, mantis and rebel sectors are great for cash. Engi have drones which suck for stealth based ships, so avoid them. Zoltan sectors can also be tough since they slow your crucial first salvo. Rock ships have missiles so pick rock sectors if you have defense drone or stealth. Civilian sectors are a trap unless you are really in need of a store. Nebula zones are generally not a great choice, but still better than civilian.
Go to homeworld sectors, since they offer better rewards.
Do quests and prioritize distress signals.
Go to abandoned sectors only if you are planning a boarding run.
If you are in an abandoned sector, keep 40 scrap in store at all times since you can use it to buy a Lanius from a common event.
Buy a second Lanius from a store. You now have the best boarding team, which trivializes a lot of encounters and lets you casually board attack drones.
Get a cosmopolitan crew makeup to take advantage of blue events and deal with situations. Humans are the worst since they offer nothing special. Rockmen are only good as pilots or doormen. Slugs are good, but you only need one. Engi, Zoltan, Mantis all make the best crewmembers but a duo of Lanius are very overpowered in a boarding setup. Crystalmen are on par with Lanius for boarding but very rare. Use their lockdown ability in every fight.
Put two Zoltan in your shield room, prevents the enemy from ioning down your shields complete. A solo Zoltan goes in the engine room.
Engi should man sensors or doors so you can have them roam and fix problems if needed, same for Mantis.
Vacuum suckers that board your ship. Game the way the AI moves around, you can easily manipulate them into running in circles in vacuum rooms, beating at doors. Boarders are generally not a serious threat.
Upgrade piloting early on.
Upgrade doors to level 2 depending on your crew makeup.
Juggle power between systems as needed. Did your defense drone just shoot down their missile? Good, depower it because you won't need it until their next shot. Enemy ship has only one laser but two bombs? Depower shields down to 1 pip and boost engines.
Pause all the time, stutterpause during their salvo to immediately repair systems hit by their weapons or open doors to extinquish fires and kill boarders.
Play the game on easy mode to unlock ships you don't have. Some of the achievements are extremely annoying or not easy to achieve on the A ships, so just get them done on easy mode and then come back to them on hard once you filled out your roster.
Buy crap you don't need. You don't need level two doors right at the beginning of the game, you also don't need three shield pips in sector two, these are luxuries that make you feel safe but prevent you from building a good offensive capability.
Upgrade your reactor except for the bare minimum needed. You don't need to power oxygen throughout your fight, you don't need to power stealth, shields and engines at the same time. You don't need to power your defense drone except to stop an incoming missile or drone. Save scrap, scrap is life.
Buy crew from stores, except in some unusual situations or if you're in the market for Lanius. Most runs will fill result in maxed out crew even if you don't buy any. Engi B can be an exception to this rule.
Be tempted by fancy slow firing weapons like the Glaive Beam, Burst III or the Vulcan. These come into their own lategame on stealth ships (or in the rare case where you luck into a preloader), but they're a liability early on. Get reliable, fast firing lasers like Burst II, Flak I, and things like that.
Upgrade Fed C's flak artillery, it's garbage.
Leave your crew in the medbay except when they need to heal. If the enemy hacks your medbay you just lost a crewmember.
Forget that ships can jump away. Once you've dealt with an enemy's weapons, fire a few shots at piloting to prevent their escape.
Perform risky boarding operations on ships that are about to jump away. You will lose your crew even with a clonebay, just accept the loss unless you're really sure what you're doing.
Look into the great eye. You might lose a crewmember even with a clonebay.
Accept offers of surrender, since they are nearly always worse than what you get if you kill them. Only exception is if you're really low on fuel and they are offering fuel.
Buy missile weapons. They are almost never worth it. Bombs are better since they bypass defense drones, but only go for them if you're boarding and have mind control as well. I generally don't buy bombs, but sometimes keep them if I find them in events. Missiles are shop trash.
Fight at pulsars. Pulsars are one of your biggest enemies. Ion storms are also really bad news.
Be afraid of boarders. Boarders are mostly a joke and you can pull pranks on them by exposing them to space.
Worry too much about enemy mind control. This can be annoying but you can usually juggle in some other crewmembers to keep the mind controlled one occupied so they do not destroy a system. Focus on destroying their weapons and other things that pose a more real threat instead.
Forget to turn oxygen back on at the end of fights.
Use ion weapons in most cases. Ion weapons don't do anything that a good laser salvo doesn't do better, although they can sometimes be a decent supplement to a beam setup.
Rely on the pike beam as your primary damage source. The problem with the pike beam is that it can only do 1 damage per system, which will prevent you from knocking out weapon systems quickly in the later sectors. You want concentrated fire.
Forget to have fun with the game. Sometimes going for a weird setup, or using a crappy ship can be more fun than building another killer gunship or mantis boarder. I've had a lot of fun with firebombs and suffocator ships, and some of these setups are good against the flagship.
Try to get the Crystal event chain on any ship other than Rock C, which comes with a Crystalman. For Rock C, the chance of getting and completing the event is once in a blue moon. For all the other ships, it's like finding a flying horse on the same day you win the lottery.
Try to unlock Rock B and C on hard mode using Rock A. Rock A is the worst, most tedious ship in the game and Rock B isn't really much better. Rockmen and missiles are awful. Get those achievements done on easy mode to unlock Rock C, then use easy mode to get the Crystal ships. Don't be a masochist.
Underestimate the weapon charger augment, these stack and are very useful in getting your salvos off fast or charging up chain weapons or vulcans.
Keep useless augments like the DNA bank, emergency respirators, rock plating, system casing, slug repair gel and other utility crap. Sell them all, they only take up augment slots. Also sell the zoltan shield at the last store since it has almost no value against the flagship, buy engine bars instead.
Use attack drones. Attack drones are all bad.
Use shield drones. One exception is the Stealth C special shield drone, which you might want to hang on to if you can combine it with stealth.
Use defense drone II, defense drone I is better, requires less power and does not waste shots on lasers.
Use any of the boarding, anti personnel or repair drones. These do not add much. The only good drones are Defense I, Hull Repair and maybe Anti-Drone if you're being generous.
Buy drone control as your first system. It's too defensive and that 85 scrap is probably better spent on a weapon or hacking. Drone control is not horrible but it's more like a fallback option.
Get comfortable. Even if you have a cool loadout and are cruising through your run, there is always a type of ship that can still hurt you badly, or an event that can seriously mess with you.
Listen to people who say hard FTL is impossible. It's doable, fair and fun if you learn about the variables in the game.
Waste your time in normal mode. Once you've unlocked stuff on easy, go straight to hard! Normal does not make for much of a difference, and hard is where the real game is.