Hard-Science Heroic Fantasy. It seems like a contradiction of terms, but it really isn’t.
In a fantasy novel everything should work and be technically feasible. Weapons, armor, combative techniques, building methods, transport, medicine and what have you. To me this is simply good craftsmanship and due diligence. If details like these are blatantly wrong it’s going be off-putting to many readers and break immersion. In the Information-Age all the data you need are literally at your fingertips via the Internet. There’s no real excuse to get these things wrong. Mind you they don’t need to be exactly historically correct; we are talking about fantasy after all. But they have to be plausible to a wide variety of audiences with a wide knowledge-base. It’s better to be vague than to be wrong.
Hard-Science SF is based in real science or theoretical science and is often centered around the ramifications of an emerging theory or technology. The rule about the Hard-Science SF is generally ‘We’ll give you one,’ meaning you can have one ‘magic’ technology, a technology that doesn’t conform to known scientific principles or that you don’t explain. In the past this usually meant a faster-than-light drive system, though now of course there are actually people studying warp drive. In a Hard-Science Fantasy the ‘One’ given would be not merely a magical technology but actual magic.
Given that the author has paid attention to the details, what would make a Heroic or Epic Fantasy ‘Hard Science?’ The introduction of a technology that drives the story or that is necessary to the story. This technology can be well-established or the story could concern the chaos generated by the introduction of the technology. The point is that it changes the world, either shaping it to it’s present form or disrupting the established order of things. In either case the story cannot happen without the technology.
Hard-Science Fantasy is not a common genre, but it’s out there. Often the transformative technology is one form of firearm or another but it needn’t be. It is felt that the introduction of coffee, a stimulant, to the west spurred the Industrial Revolution because people drank it instead of a depressant, alcohol. Any number of other technologies could have huge effects on society. What would the effect be of introducing Gaslight or even electrical lighting to the culture of a medieval city?
It’s not always implausible to introduce an anachronistic technology to a fantasy setting. After all the Romans could have built repeating rifles if they knew what the were and wanted them badly enough. The ancient Greeks could have and nearly did build steam engines. Making electricity is easy enough if you know that you want to. So think about and toss in an anachronistic technology, add some swords-and-sorcery and you could really have something.