Are Hard-Boiled Dominators supposed to be that hard? There's no way I could have taken out a system by myself yet, not with engines going 450 and two launchers in my starter ship.
Hard-boiled are quite manageable - they're not hard, they're pretty much right, because on easier difficulties AI rangers just win the game without you and that's no fun.
Here's an easy & simple guide to it:
1. Obviously, you must start with 2x rocket launchers - anything less is not adequate for the task. I suggest engine as a second piece of equipment & attack+defense skills as they are worth more XP than non-combat XP and there's a real shortage of XP in the beginning of the game. That leaves you with faeyan or peleng start - faeyans are obviously better since their ship has afterburners & their equipment is more durable.
2. Do the tutorial, at least to the point where you're advised to sell some hardware tech on another planet - it's very important that you sell all your unneeded equipment for this (anything except launchers, engine & fuel tank) so you can buy as much goods as you can. Use afterburners to deliver the goods (use afterburns for everything, actually - use a cheap, lightweight, upgraded 1st generation engine & afterburn it indefinitely, it's much cheaper & faster than to use a more advanced one) - it is important to act as fast as possible so AI ships won't be able to buy much of your precious tech. If you're really into it, you can save scum a bit until the point where during this quest 2 planets are as close to each other as possible. Make these runs for as long as the good prices last.
Also, to prepare better for the run you may either buy some additional meds before delivering them to the sick planet or gather some minerals in the space to earn some extra money - the more money you'll have, the more you'll earn. if they'll offer it to you, you may also do a tutorial planetary battle quest on the third planet in the system (other than these quest two) - reward money will help.
Depending on your luck, this process will net you 10 to 25k credits.
3. Now you will have a wee bit time before all youre base will belong to the dommies. Try to use it effectively - do some quests if they're available, explore some black holes if you can, search for better gear (you're looking for any lightweight pigamar one, with bonuses to missiles, it's kinda broken in early game) and modules. In terms of modules you look for cheap ones that give +10 to the rocket launcher power - since each salvo fires 3 rockets, the summary damage increase is 30 and that's totally nuts. Also, buy some star maps because in a short time you won't be able to do that for a while.
If there's a business center, buy yourself a life insurance (you should always be stimmed up with some combat skill enhansing drug, the best one is gaalistra of time, obviously, and insurance saves you ton of money here) and try to take a credit from there just before dommies invade the system where it hangs & destroy it - mind you, you must take it not during invasion (they won't give you money, don't even hope), but just before it. The reason is that when all business centers are destroyed all your debts to them are nullified so it's more free money for you and you need them.
Oh, and if there's a pirate station, you may wish to buy some camo if you can afford it.
4. After a year or so, dommies will take all of your systems one for one and you'll become deadlocked in your homeworld. Do not despair - it's perfectly normal for a hard-boiled playthrough. Besides, dommies won't attack you with deadly force - there will be no full-scale invasion, it's just Keller who will be pestering you again and again. Now, first objective is earning money (between his attacks). Basically, you have two options:
a. Get yourself a mining laser and hunt for some asteroids. Use laser to break them - it's not called "mining" for no reason, you'll get more minerals this way. Sure, the system will soon get oversaturated with them, but even 6-7 credits a pop is better than nothing. Besides, if your luck setting is not awfully low, you'll often get a credit bonus for destroying the asteroids, so it's not that bad of a deal.
b. Use the "luxury triangle" technique. How it works. See, planetary economics in rangers works by a simple "supply/demand" model - the more stuff the planet has, the less it pays for it and vice versa. Therefore, what you need to do is to concentrate all luxury present in the system on one planet - you will sell it at an average price (even high if you'll time it right), then, after a while, it will become pretty cheap. You buy it back and haul it to another planet - since, thank to your efforts, there will be no luxury items on it, it will buy yours pretty high. OK, you wait 'til it gets cheap again and then drag it on to another planet... You get the point, right? Do this ad infinitum and you'll become an millionaire easily. And sure, you can do this with every kind of merchandise, it's just that the luxury has the best cargo space/profit proportion.
5. Don't forget to scan the uninhabited planets for good - you really, really need good artifacts & modules. After you'll scan the planets of your homeworld (which shouldn't take long), do a blockade runs inside occupied systems. Basically, you jump in, fly to the planets on afterburners, drop the satellites, wait for a couple of days (as soon as you land, dominators get sad about not being able to kill you and fly away from the planet, back to their patrolling routes) then lift off and either fly to another planet (if you have enough satellites & engine durability - to gain more satellites easily, buy them while under duration +tech drug, you will be able to get up to 7 of them fast this way) or back to your homeworld. After the scanning is done, collect in a similar manner.
You also may do a blockade runs to the systems that have a black hole inside of them, but that's a bit more luck dependent - there's no guarantee that the hole will spawn in a safe location and not in the midst of dommie swarm & that the exit point will be in a jump range from your homeworld.
6. Try to do all quests that you're offered - money are not that relevant, but each quest gives you precious XP and a chance to win artifact/module. Well, there will be 2 types of them - planetary battles (annoying, I know) & guard the system/ship for X days. I prefer to do the latter on the easiest setting - you lose some money, but, without save/scumming, you never know when keller shows up and it's hard to repel him without casualties.
7. Now, you will have to occasionally repel Keller - as soon as you have money to repair your ships and restock your missiles via paragraph 4, you'll do fine, just remember one rule of utmost importants: PROTECT STATIONS AT ANY COST. Seriously, none of them should die or you're really, really screwed up - med stations is gone, no stims for you (meaning shooting that doesn't do shit) and if you're sick, you become absolutely worthless in combat. Ranger station gone, no missile-upgrading modules for you and no good equipment for you. Science station gone - no loot 2x money for you, no upgrades for you. Basically, they're crucial, so if you see any of them in low HPs, dock to them, buy permission to upgrade them and repair them - yes, it will cost you a lot of money (always keep a spare 50k credits for this), but there's no other way. Stations are your lifeline.
Other than that, it's pretty easy - Keller's ship are pushovers and there's not much of them, so, with your uber-upgraded missiles & tanking done by other ships in the system you should do just fine. The hardest time is when all the military men die - see, your system slowly spawns military ships until it has a maximum number of them, after that, it sends them to liberate a nearby systems (i.e., to die pointlessly, until a certain point, at least). And that leaves you with a window of vulnerability where you will have a couple of merchant ships to help you and that'll be it - be prepared. Also, you can accompany armymen to their doom - just gather the loot until they die then run back to your homeworld as fast as possible. And that's the way you'll liberate your first system - by accompanying them to battle (somewhere in a year 04-05; you can also do it solo, but it takes more time - year 08 or so, unless you're bloody lucky with artifacts & items).
One other thing to add is that, with some patience & skill, you can slaughter keller inside his black hole by using just 2 starting missile launchers - just fly in circles and spam those missiles at him, but don't miss the respawns of healing bonus in the middle (it's especially easy with droid junior). But I'm against it, actually - of you kill him, no one will attack you, and if no one attacks you, where will you get loot and XPs?
One other trick is to fly inside Keller's black hole while he still floats in your system - then, instead of his boss level, you will find yourself in some usual black hole level, with usual artifact prizes, but the important thing that the exiting point won't be random! You'll exit to your homeworld system, just at the point you've entered it. Now, there's a catch here - if your hull points are low, Keller may blast you to smithereens as you rush to the black hole (or exit it), but, if your speed is good and you time it right and you're not escaping the hole in low HPs, you can avoid that possibility.
Well, that's pretty much it - just do these things and in year 04-05 (maybe a bit later, that depends on your surrounding worlds) you will reclaim your first system (at the very least, you will get powerful enough to combat dommies via missile tactics, so you will get lots of loot and XPs) and after that it's just a snowball.