Here's a video that perfectly breaks it all down but the TLDW is this:

The game has difficulty modifiers that can be added (enemies get more shields, you can't heal, etc.). No one had ever beaten the game on max heat (all modifiers) mostly because of a modifier that restricts your time to complete the game. The problem isn't killing everything - it's killing everything fast enough to beat the clock. There's basically only one build in the game to get the DPS needed but you need a series of exceptionally lucky events to happen to make it possible. This run was thought impossible not because it's literally impossible but because it was unlikely for someone to put in the mind-numbing effort to grind for hundreds or even thousands of hours just to get potential runs. The crazy thing is that Angel got the insane luck needed for a run after just like an hour of serious attempts.

Ana Diaz does a pretty good job of explaining it here

A 64-heat run is a run with EVERY ingame difficulty modifier switched on, so enemies are tougher, more numerous, and ignore the first couple of hits, whilst the player is weaker, barely heals, has no invincibility frames after getting hit, and can't use most of the upgrades earned by unlocking things between runs. Oh, and all the bosses are entirely reworked, harder versions including an entire third phase for the final boss. What REALLY makes it difficult though, are two specific stipulations, because they're heavily influenced by RNG (random number generation). Through a run, the player is given a series of powers that modify and upgrade their abilities. Each time they complete a room where a deity's power orb is located, they get to choose between three randomly selected powers associated with that deity. This is limited enough to make a player have to think on their feet, but enough to allow an experienced player to create a build (a suite of powers that all work well with each other) quite easily. Heat 64 reduces the choice to one item out of the three. Basically, aside from the occasional collectible reroll, your build is almost entirely at the mercy of the random number generator. Get the wrong rolls? Your powers are going to suck and you're going to either die quickly or be slowed down by a low DPS (damage per second). The other is that under Heat 64 the player has 20 minutes to complete the game, rationed out as 5 minutes per region. This is an extremely slim number even if you're playing normally, but with the full Heat 64 suite of limitations it's utterly hellish. The player needs to do everything they can to get through quickly, and in many cases just needs the game's RNG to straight up co-operate. The biggest and most obvious example here is that the final stage takes places through a series of 5 tunnels, one of which has the item needed to progress to the final boss, whilst the others all have minibosses. A player can have a perfect game up to that point, but then find the item too late, thus guaranteeing that the clock will run out during the boss.
The RNG is extremely unlikely, and the skill level required to even perform at this level is incredibly high, so the combination of the two seemed extremely unlikely.