So while the gold farming exploit is there for you to use, with a bit of practice and planning, this is very doable without the need for farming a bunch of gold on one character. Even if you do farm a ton of gold, it won't help if you don't know how you should be upgrading or at what level/life you can reasonably take on a particular area. That being said, here's an outline of how you can go about doing this achievement:
1. With the first knight you start as (Sir Lee, lv 0), you want to kill the first boss in the castle, Khdir. Ideally, you would explore the whole castle and then kill the boss, but you run the risk of not having enough health when you go into the fight and while not getting hit is relatively straightforward with that first boss, things happen. So long as you start the fight against Khdir with more than 86 health, you can take two hits before the next one will kill you. Once you've beaten Khidir, continue to explore the castle and start exploring the forest as well. The more gold you get and the more chests you open, the better.
2. The general strategy going forward with each heir is to explore the different areas, open chests and acquire a heap of gold until you're feeling confident in your ability to take on the next boss. The bosses themselves are relatively straightforward to beat I'd you've already played through the game before, more so if you've beaten the remix versions of them (which you DO NOT need to do for this achievement). In general, I found that if I was able to defeat most enemies in an area in 1-2 hits, I was good to take on the boss. That being said, just because you're feeling confident in a boss battle doesn't mean you stop exploring to make a beeline for the boss door in an area. With every run, you want to explore and get as much stuff as possible so that if things go sideways during a boss fight, or if you overestimate how strong your character is, then at least you still found some new blueprints and got plenty of gold. You need to be taking in at bare minimum 2500 gold with each death early on.
3. When it comes to upgrading your stats and gear, it depends on what class you like to play. My advice however, is to keep things basic and try to stick to using either the paladin or the barbarian. After your first death, you should be able to unlock the following from the mansion:
Blacksmith -> Health 1 -> Paladin -> Weight 1 -> Enchantress -> Architect -> Barbarian King/Queen -> Strength 1
While you won't use the architect, you need to unlock him so that you can buy the strength upgrades. I know people will suggest unlocking the Shinobi class, as it does a bunch of damage, but you lose a ton of health in the process, so I personally found that it wasn't worth doing. If you want to run a knave build, you can unlock the Shinobi to the get access to the critical upgrades (both crit chance and crit damage), but if you don't unlock any additional classes beyond the starting 4, you've got a better chance of having an heir that's a class you're actually good with (and even then, there's still a chance you wind up with 3 mages).
Even though you're taken to the manor screen upon choosing an heir, you can exit it and talk to the blacksmith and enchantress first to buy equipment and runes before spending your gold on stats. In terms of equipment, you'll want to use stuff that gives you the most strength, the most health and the most armour, depending on what blueprints you get. The blood set give you vampirism at the cost of health, so make sure that if you're going to use it, you upgrade your health to negate the loss from the gear. Other than that, it depends on your build. Since I was focusing on using the barbarian and paladin, I didn't bother buying any bracers until I got the guardian bracers, which gives you armour. The other bracers only increase magic damage, which I wasn't using, and I didn't get the blood bracers for a while.
With the enchantress, she'll always have a vault rune and a dash rune unlocked, all the other ones you'll have to find yourself. Ideally, you'd have those two runes and then 3 vampirism runes to get health after every kill, without needing to use the blood gear and suffer a health penalty, but the grace, haste, bounty, balance and retribution runes are all useful too, just depends on what you get.
As for the stat upgrades, you want to mainly focus on upgrading strength and health. Only upgrade weight when you can't equip a new piece of gear, and only upgrade it to the point where your weight stat will be maxed out with the new item in order to conserve as much gold as possible for other upgrades. If you've got enough money for other upgrades, but can't afford to upgrade strength, health or weight and there's no other runes or gear you want to buy, you can either not spend it and lose it all when you go back into the castle, or feel free to increase your mana or magic damage, either option is fine.
4. Make sure you know how to fight each boss and what will be more effective on certain ones over others.
Khidir: Like I said before, you want to fight him with the first level 0 character. Stay on the floor and dodge his attacks, jump up and attack when you're in the clear. When he starts his spiral attack, avoid the projectiles while moving around the room and if you have to jump over him, do a downward strike, otherwise you can't clear him and will take damage. And again, have more than 86 health going into the fight so that you can't take two hits before a third one will kill you so that you have room for error.
Alexander: Vampirism and high damage will make the fight very easy and consistent. Try to stay below the boss, because when he launches his beam attack, he stays still and if he's close to the ground, you can avoid his attack while whacking him from underneath. If you can 1 shot the additional skulls he spawns, you'll be able to keep your health topped up the whole way through.
Ponce de Leon: The barbarian shout is handy, but if your damage and health are high enough as a paladin and your movement around the arena is good, you'll be fine. Stick to the edges as much as possible, use your dash for lateral mid air movement if you get caught in a circle of fire balls and also use it when Ponce stops in place to prep his charge attack. It'll put you just beyond where his charge ends, so while he recovers, you can get a few hits in for free. If you have a retribution rune and get hit by a spike ball floating around the arena, it should get destroyed, giving you more freedom to move around.
Herodotus: Much like Alexander, high damage and vampirism will be your greatest allies, but only if you're patient. Herodotus spawns a mage every time he splits into two, and while the slime balls can bounce around quite a bit, they're not as much of a threat compared to the mages and their rock spike attack. Be patient, do enough damage to make Herodotus split and then immediately kill the mage that spawns. Then, focus on one blob, make it split, kill the mage, so on, so forth. Don't try and be even handed with it, focus on one blob until it's permanently gone, then do the next. You'll find that if you stay higher in the arena, you can effectively engage in a one on one fight with a blob while the other blobs try to figure out where you are. Again, patience and deliberate targetting will make it a breeze.
Johannes: You'll want to be very good at dashing along the ground to win this fight. If you can replace any vampirism runes/gear with other stuff that has better stats, do it so that you have as much of an advantage as possible. Don't bother with the paladins shield either, it doesn't seem to block this guy's attacks. Jump the dagger burst attack, stay under him and dodge his axe throws when he jumps up and don't pursue him if you hit him, as he'll more than likely dash backwards and throw a blade wall down. Backing yourself into a corner actually works decently well if your character can knock him back when you hit him (there's a trait that your heirs can have called Muscle Wk which prevents enemies from being knocked back when you hit them) but more than anything, being able to hit and dash away is what will make this fight doable.
The Fountain: Surprisingly, the strategy of hit and dash is pretty good here too. Try to stick in the centre of the arena, because if you can get the fountain to do his ground spear attack, you can easily jump to one of the platforms you have to strike to make appear and stay completely safe and once the spears start to drop back into the ground, you can hop down and get a couple of free hits in. When he's moving towards you, hit him and then dash away and just pay attention to what he's doing. If he stands still and his sword flashes, he's about to attack, but his position will determine what move he does and you should know what to expect.
So yeah, there's quite a bit to this achievement, but it's very doable without needing to use a gold farming exploit, provided that you know what you're doing. Hopefully that outline helps a bit and good luck to you if you're going for this achievement, cause you'll definitely need some with this game.