Uhh, that's a pretty weird question about which Primal-Groudon, Scarf Kyogre and Arceus-Ground counter Calyrex-Shadow.
Starting with Primal Groudon, never use it to counter Calyrex-Shadow. Of course Primal Groudon OHKOes Calyrex, but it isn't going to survive a Life Orb Astral Barrage unless Sp.Def invested. Calculations:
252 SpA Life Orb Calyrex-Shadow Astral Barrage vs. 0 HP / 0 SpD Groudon-Primal: 333-394 (97.6 - 115.5%) -- 87.5% chance to OHKO
On the other hand....
252 SpA Life Orb Calyrex-Shadow Astral Barrage vs. 0 HP / 0 SpD Arceus-Ground: 261-308 (68.5 - 80.8%) -- guaranteed 2HKO
While it does:
252 Atk Arceus-Ground Earthquake vs. 0 HP / 0 Def Calyrex-Shadow: 186-220 (54.5 - 64.5%) -- guaranteed 2HKO
So, none of these two check Calyrex Shadow reliably. Going to Kyogre, Scarf Kyogre can beat it easily.
252 SpA Life Orb Calyrex-Shadow Astral Barrage vs. 0 HP / 0 SpD Kyogre: 227-269 (66.5 - 78.8%) -- guaranteed 2HKO
252+ SpA Kyogre Water Spout (150 BP) vs. 0 HP / 0 SpD Calyrex-Shadow in Rain: 448-528 (131.3 - 154.8%) -- guaranteed OHKO
Also, if you're Timid, then you can outspeed Calyrex-Shadow and land the KO. But due to the prominence of Primal Groudon, Scarf Kyogre is useless. The best check is Pursuit Pokemon, most notably Tyranitar, which checks Yveltal (non-Focus Blast) and Mega Rayquaza (non-Earthquake) apart from Calyrex-Shadow, by Pursuit trapping it.
Hope this helps!