Ironically, the number of Shadow Quagire’s goals matches that of non-Shadow in Great League PvP. 112.68 Def with 163 HP recommended minimum, empowering Sableye 0-0 (Mud Bomb) & 1-1 (Aqua Tail), while boosting Gligar 2-1, Umbreon 1-0, and Powder Snow Shadow Alolan Ninetales 2-2. The very high Def helps against the high Atk weighted Sableye, and may power the Froslass 0-1. The top Def of 0/14/8 and 0/15/6 can catch Pelipper (0-0), mirror focus on Froslass (114.15-114.46 Def), and possibly Lickitung suddenly, but the drop of -HP can cause problems in the Sableye matchup.
Given how hard it is to get Shadow Quagsire in bulk, you may have to settle for a low bulk. 110.26 Def is a soft low this time, stick to Shadow Alolan Sandslash 1-2 (Mud Bomb) and Emolga 1-2 (Mud Bomb), while avoiding Carbink’s Rock Throw Breakpoint (reinforces 0-1, 1-2, & 2-2) . Combining this low stat with 110 Atk can make Medicham 2-1 (Mortar Bomb), Shadow Venusaur 1-0, Noctowl 1-1, Cofagrigus CMP, and Carbink 1-2 (both) & 0-2 (Mortar Bomb. ).
If you really want to scare Carbink, 111.89 Atk enables Shadow Quagsire to drop Rank 1 Carbink to 1-2 with Aqua Tail or Mud Bomb, and to 0-2 with Mud Bomb (112.22 Atk vs Best Buddy). At this Breakpoint, Mud Bomb Shadow Quagsire will be 1 of 4 (IVs to him) non-Steel-type Pokemon to defeat a Carbink with 2 shields without spending a shield or fishing shields. Neither metal types nor Clodsire will want to fight Shadow Quagsire either. Having a high stack is still recommended, as the Atk weighted Carbink can scan the script for you. Additionally, having >109 Def can keep Shadow Venusaur 1-0.