Despite Quorthon's colossal influence on extreme metal, it would take 15 years for a full-fledged musical homage to the first Bathory album. Prior to Into Fire, I'm unaware of any truly blatant early Bathory worship--the Viking era always fared a little better in terms of tributes. While the '90s Norwegian and Swedish black metal scenes were built largely on the progression (or more often, regression) of ideas and elements culled from first 3 or 4 Bathory albums, there weren't any truly accurate pastiches aside from some particularly well-done covers or the odd isolated influence in individual songs. Even in the '80s, the notable instances of Bathory influence came alongside Venom, Hellhammer/CF, Sodom, and/or general thrash and speed metal influences. Nowadays, with the proliferation of '80s emulation, black'n'roll, and punk-infused black metal bands, it's somewhat easier to find music that approaches the Bathory s/t sound*, although again, finding early Bathory as the sole or overriding influence is rare--most of the current recordings approaching a '83/'84 Bathory-esque style owe just as much to Venom, Motörhead, and Bulldozer as to Quorthon.
There's no ambiguity with Into Fire; within a few seconds of the intro ending, it should be extremely obvious that one particular album from 1984 provides the musical template here. The vocals (which show up right away) aren't anything unusual in a general black metal context, but they impede accurate Bathory emulation a bit, as they sound slightly artificially modulated and overly screechy. The title track is strange, as it's just "Armageddon" with minimal changes, so it seems somewhat unusual it's not just a proper cover version--why go to the trouble of creating a new title and lyrics if you're going to play the main riff unaltered anyway?
Otherwise, the earlier tracks on the album are very good at capturing Bathory stylistically, although compositionally the songs are quite simple, with riffage that seems on the primitive side even by early Bathory standards! The Into Fire version of "War," titled "Rise of the Dead" (yeah...) stands out as the best track. Obviously, this can't hold a candle (much less 13) to the Bathory album, but taken in context as a musical homage or compared to more modern sounding black metal recordings, it's still quite enjoyable. However, the final two tracks are a shame because they suddenly deviate from the formula. "Witchride" is a slow/mid-paced number which feels very out of place--I assume it's an attempt to provide some tempo variety, but it sounds more like a plodding track from a minimalist black metal band than anything approaching "Raise the Dead." Closer "Final Offense" is even worse, largely dispensing with the '80s stylings and sounding far more like some generic Bathory-influenced '90s Nordic BM track.
Of course, there can be no discussion of Hellfire without pointing out their MYSTERIOUS ANONYMOUSBAND status. While it would be kind of interesting to know who's actually behind Hellfire, the main reason I want someone to spill the beans is to shut up all the ridiculous uneducated guesses being made online. I know, I know, the ruse is that Hellfire is actually from Sweden...But teenage black metal authorities insisting it was the Nifelheim twins? Or the Nödtveidt brothers? Seriously? I'd personally always heard that Hellfire was an old school diversion for either the Falkenbach fellow or one of the Veles guys, which seems plausible given the No Colours connection. But ultimately, Into Fire is what it is, and given the persistent mystique of early Bathory, Hellfire's anonymity is only fitting.
*"Necromansy" cover notwithstanding, I will say while they're not 100% Bathory sounding, the older Occult Burial material (particularly the demo) is probably the most consistent stuff I've heard at capturing the aura of Bathory's debut, even moreso than Hellfire at times.