Now, this is just the method in which I succeeded in clearing Hero 300 on the hard difficulty. As this is an RPG, there's always more than one way to skin a cat. I'm gonna point out what level I was at approximately for various points of the run but obviously it won't necessarily be the same for everybody, and there's always a chance that one could do it at a lower level at various points, as is the nature of this game.
As the time doesn't stop while you're in towns/villages/etc, you basically have to path out what weapons and armours to purchase and when to buy food/herbs along the way. The way I see it, the ultimate goal, in my mind, is to purchase the final weapon and helmet before moving onto the point of no return.
So to begin, make your way to the town north of the castle near your starting point. Buy the Wooden Sword and make your way to the castle up north where the Knight and Sage are being held. Battle around the castle until level 4 and then make your way into the castle and save the Knight and Sage. From there make your way east to the 2nd continent.
When you get to the castle nearby, top up your HP with the food and pick up a herb as well. If you have the cash, pick up the Village Garb too, but otherwise you can always just claim it on the way back from grabbing the princess, as the Knight will do an incredible amount of attack for you and prevent you from suffering too much damage at this stage. Once you've left the castle, walk your way east towards the forest where the Princess is. Don't worry about stopping in the village on the way there, just make a bee-line for the princess, completing every battle along the way. Then walk your way back to the castle, top up on HP again, and pick up the Village Garb if you didn't the first time around, and make your way north to the next continent. I was typically around level 13 at this point.
You'll come across a town. Purchase the Flower Crown, and do a little level grinding next to this town until you get to level 20. I found that this was the best place to do your level grinding to ensure victory in the end. Once at level 20, top up on HP in the town, and make your way to the village up north via the western path (you'll gain a couple more levels along the way too). Once there, buy the Battle Boots, Silver Mail and Flash Shield. Now make your way directly south from here towards the Evil Lord. Dash attack him, using your herb if necessary (although I didn't need to when I'd tested this). Then make your way back north to the previous town, top up on HP (and herb if need be), and continue north to the next continent.
The level grinding on the previous continent makes the rest of this pretty straight forward. Head straight through the 1st cave, dash attacking the enemy in there. Once out, head into town and top up on HP, then make your way to the 2nd cave where you'll meet the Bandit Trio yet again. Dash attack them and you'll make it to another village just outside the cave. If you have the cash at this point (you should, but you may end up a little short), purchase both the Brave Blade AND the Brave Crown, along with the food (and herb if need be). If you don't have the cash for both the Brave Blade and the Brave Crown, then just pick up the Brave Blade. Dash to the tower on the left hand side and dispose of the Dark Knight. Head back into the village and top up on HP (herb if you used it, Brave Crown if you didn't pick it up the first time) and dash your way to the right hand tower where the Reaper awaits and dash attack him to pieces. From there, dash straight to the tombstone in the middle, which will prompt you with a message along the lines of "this is the point of no return". You'll be teleported to the last section of Hero 300. I was usually at level 37 by this stage.
Top up on HP here (and herb if need be) and just grind on the Hell Mantle (make sure to dash through them, you're more than strong enough to not have to worry about them at all) around the bridges. I recommend until about level 45 (although obviously you can stop at a lower level considering the "YOU > EVIL" message comes up at 40, but 45 I found was more than safe enough to succeed without giving away too much time and putting in too much effort on the final bosses). Once you've grinded out to a sufficient level, head back and top up on HP yet again, then dash straight for the castle in the north. Dash attack the boss, using the herb as needed. Cutscene, HP/herb top up if need be, dash attack the final boss.
Achievement will pop on the results screen which shows your time, and your Hard Clear title being achieved :)
This is by no means the most efficient way/fastest way to accomplish this, but this is in my opinion at least a safe method to complete this with time to spare (as is the goal of this game of course). If you're looking for a speed run of Hero 300 hard, this is definitely not the path to go for.