Fear Catalyst's solution is definitely a solid build! But I feel I have a built that might make this slightly easier, thought it does require a little bit more RNG.
"Hard" mode simply adds more threats. That being Natural Hazards, Elites, and those damn Jump Suppressors, among other things, all while offering less resources.
The thing that will make this easier is your Enhancements. The Enhancement set up I used I found watching the World Record speedrun. Using it, on my second try I was able to finish my run in only 25 minutes. It's slightly more aggressive and relies decently on RNG, as well as kind of just rolling with what you find and not scavenging for resources or crafting damn near anything.
The Enhancements I used are as follows:
Ancient Weapon: This Enhancement replaces your Primary Weapon with an ultra powerful weapon. But on the other hand you do not have any missiles and every shot you take brings your Hull HP down. This Enhancement is the bread and butter of this build. It is so incredibly busted. I could one shot almost anything from often up to 3kms away. I could usually three shot elites. And Corvettes and Drone Ships were down in less than 5 seconds. They also make frigates not as difficult if you're careful.
Equalizer: After each jump the hull is set to 50%, regardless of if you're above half or below. The reason this is so helpful is a few reasons. First off, on Hard you might be getting damaged a decent bit, especially considering your Weapons does damage to you. This makes it so you don't have to constantly try to find nano bots. And if you do ever get low, just make sure you leave the fight and warp out. This run also can rely heavily on using Lucky Jumps, where if you Jump with no fuel, if you have Lucky Jump Chance at max you have a 60% chance of taking no damage, but a 40% chance of being damaged during your jump, this makes it so if you do take damage during a Lucky Jump, you are always mitigated at a 50% Hull.
Headstart: Start off in Sector 2. Not much explaining, further start means less fuel you need for your run.
I used the Sentinel ship from the DLC fully upgraded, but really any ship that is close to max or max, but the Gunship, will do (because it is slow, and you want a decent amount of speed). My pilot was also nowhere near max, but there are a few key perks you definitely want maxed to make life easier. Those are follows;
Lucky Jump Chance
I also have some equipment recommendations that helped me along the way. I was using the Sentinel as stated, so had access to EMP, which is great for disengaging combat. Though if you do not have the DLC or that ship Maxed, the other ships will be fine. Scout probably better due to cloak escape.
Other than that the equipment I would recommend crafting are as follows:
The reason for these two is simple. The Teleporter lets you jump around the map super easy and quickly, which is good for escaping fights. The Tractor Beam allows you to quickly pick up resources from far away rather than having to fly right next to it. Really just a little thing but it helped. Teleporter is first priority though. If you're lucky as well you may find an Emergency Shield, which can prove very useful.
Remember the goal of this build and run is not to scavenge but to get the hell out of there. Don't feel bad if you killed one enemy and left, or even none at all. If the zone as nothing for you, just leave. It may seem like you are wasting fuel but you will be fine. On my successful run I personally never had to go for a Lucky Jump. I was confident enough killing some enemies to get fuel drops. Just choose your path on the star map carefully and you should be fine.
Worth noting when choosing a path, you may actually want to go for Zones marked with a natural hazard, because you could get lucky and get an Ancient Ruin, which can jump you forward a few zones or even a whole sector.
One last tip, if you're losing a fight and may die, you can quit and reload to retry the zone. I personally didn't have to do this on my hard run but have in the past and it can be a real life saver.
Follow all of these tips and you should find this relatively painless! Good luck!