The Hive Mind
I'm toying with the idea of making the Hive mind actually a twisted immortal Emperor class (originally) human psyker - one driven out long before the Imperium was formed when the Emperor was young.
With access to Dark age of technology ships he could have fled far beyond the milky way until he found the original species that he would spend millennia re-moulding into the Tyranids through the use of incredible genetic engineering techniques (similar to those the Emperor used to create the Primarchs).
Initially he sent groups of genestealers into the Imperium as scouts since he was still wary of the Emperor's strength but finding him greatly weakened he directed his hive fleets to begin their probing strikes on the Imperium.
His hatred of the Emperor and quest for vengeance lead him to alter his own dna to enhance his psychic powers and 'improve' his human form...
Transformed into a twisted inhuman monstrosity he now seeks the genocide of all humanoids while still nursing an obsessive hatred ( and fear?) of the Emperor which bodes ill for the Imperium of mankind...
The Hive mind is probably the greatest weakness of the Tyranids despite his incredible psychic strength - if he could be destroyed the Tyranid threat to the Imperium at large would melt away...