The Blademaster, like all the Pxet Elites can be spawned by killing trash in her general area. There is an invisible counter that ticks up and once it is high enough she spawns and the counter resets.
For the Blademaster this includes all trash mobs from the central room (big room with fountain in the middle of all 4 elite rooms) to her room and including the trash in her room obviously. Plus everything on the way to the Qinimi zone line as well as mobs between Riwwi and Qinimi. It is unclear which elite, if any, the trash in Hexxt Gkon's room count towards.