Hyperblade Catalyst in Destiny 2 appears to come from the Fire and Ice exotic mission on Legendary difficulty, with the mission timer objective started early by shooting the required crystals/nodes at the beginning. Then you need to complete the catalyst-specific blight and boss mechanics during the run, and the catalyst shows up in a reward chest at the end of the mission.

What to do

  1. Launch Fire and Ice on Legendary difficulty.
  1. At the start, shoot the 4 darkness nodes/crystals to trigger the timer; guides say the Hyperblade and Upper Hand catalysts will not progress without this step.
  1. In the blight sections, make the encounters imbalanced by throwing the needed orbs/energy into the blights, which spawns minibosses.
  1. Defeat the minibosses, then destroy the spawned central nodes/pillars with the Praxic Blade to trigger the next boss.
  1. Finish the mission, and the catalyst should drop from the end chest/reward room.

Common snag

Some players report the catalyst not dropping unless the run is done in the correct order, on Legendary, and with the timer started properly at the beginning. One community report also says catalyst progression can be blocked if you already have another catalyst from the same mission, so that may be worth checking if yours is bugged.

Practical tip

If you only want the shortest version: Legendary Fire and Ice, shoot the 4 opening nodes, complete the blight objectives, kill the spawned bosses, and open the final chest.

TL;DR: run Fire and Ice on Legendary , start the timer with the opening nodes, do the blight/boss steps correctly, and collect the Hyperblade Catalyst from the final reward chest.