How to reliably get high lvl blessings?

[Cope]

Am i supposed to roll hundreds of gray weapons and upgrade them to blessing tier in hopes of getting one?

[Hans Meiser]

No, you constantly check the shop for good high level bases, just like before. Nothing has really changed in that regard, but you have a better chance of something high level being there now.

[H.Honor]

Melk's requisitorium and emperors gifts are reliable way to get high tier blessings imho

[Halide]

Emperor's gifts now are awarded at the end of every mission, with harder missions having better odds of higher tier weapons.

[LinkZeppeloyd]

You’ll only find lvl4 blessings at Melk’s. The blues in the store only go up to lvl3

[Edge Of Sanity]

Melk's shop, higher difficulty missions with modifiers for better Emperor's gift

[Harbi]

I think the shop now only drops tier 1 & 2 blessings. Melk's shop will drop tier 3 & 4 blessings.
Bought a grey item a moment ago and cheaply upgraded it to blue, got a tier 4 blessing.

Found it in the full patch notes:

The Armoury Exchange requisition list will often see items with Tier 1 & 2 Perks / Blessings, while Sire Melk’s Requisitions will often have items with Tier 3 & 4 Perks / Blessings for characters at level 30.

[MrHugz]

Melk is your source for high tier blessings. You may find a good weapon from him once in a while, but more often I'm going to be using his shop for blessings more so than weapons.

[STABURSACNSEE]

omg I just did this.

I mystery aquisitioned a profane level 349 then spent plasteel only and got a tier 3 infernus blessing. thats a decent way to do it...