Since our removal is primarily geared towards medium to small creatures, it can really ruin our day when large creatures hit the field. That's why we don't let them. Stacking 11 ways to counter stuff in the mainboard should let us take care of our opponent's big baddies before they start punching us in the face.
Horribly Awry: Our cheapest counterspell, this gives us some control early to mid-game when we need it the most. At only two mana, we can potentially start stopping minor threats as early as turn 2 to set us up for a turn 3 play like Herald of Kozilek or Wasteland Strangler. That 4 Mana cutoff offers a surprisingly wide range, with Siege Rhino, Dwynen, Gilt-Leaf Daen, and Mantis Rider all falling just within our grasp.
Spell Shrivel: Here to take care of all the things that Horribly Awry can't reach, it comprises most of our late game defense against big baddies. The pay-4-to-ignore that it offers our opponents is usually not relevant and, if it is, it's usually because we're dealing with something small enough for our removal to handle. Two Herald of Kozileks mean this bad boy can be cast for a disgusting 1 Mana.
Ulamog's Nullifier: Running double duty for us, here is our man with the plan (as in he's a creature that also does stuff, get it? Ah never mind). He'll counter anything we need and our opponents can't do jack about it, making him objectively more versatile than both Horribly Awry and Spell Shrivel. Notably, he get's around Dispels that opponents may sideboard in to try to deal with our counterspells. We want to save him for late game when real big threats are coming in or when we know we're going to win in a turn or two anyway. He cost an arm and leg to cast, at 4 Mana and requiring us to Process two cards, so make sure to get down some Herald of Kozileks and exile some fuel before you need him.
Transgress the Mind: The look at our opponents hand is almost worth it alone, that way we always know what we need to be saving our counterspells and removal for. On top of that though, we also get to take anything with CMC 3 or higher and just deposit it directly into the trashcan, a real life saver against things we otherwise wouldn't be able to counter or remove like Gaea's Revenge and Dragonlord Dromoka. This is something to instantly sideboard up to 4 of when dealing with Dragon control. Say goodbye Ojutai, Silumgar, Atarka, Dromoka, and Kolaghan. Even better, they can't get their dragons back with Haven of the Spirit Dragon since they'll be exiled. This is a must against any deck playing big creatures or combos.