I keep seeing people post about dying to minion rounds

Here's a few tricks to help you out:

1.) If your champions aren't strong enough to beat krugs outright its because of one of two things. Either A.) You're trying to hard to force a composition and therefore are ignoring obvious 2 star upgrades in favor of what you THINK you want. or B.) You're never repositioning your units and you've got them all globbed up in the middle of the board. Move all of your units over to the isolated Krug (the one on the right) so they all focus him down first. Also, red buff is huge vs Krugs since it stops them from healing. (Katarina is good for this too, but I'm not sure you can even get a Kat before krugs? If you can though, she's great for this since she applies grievous wounds.)

2.) Dragon deals cone damage. Think Titanic Hydra. Split your team up into squishies and front liners. Put the front liners closer to the dragon on either the right side or left side of him. Put your squishies a bit further away on the opposite side. Dragon will focus down your front liners, allowing your squishies to free-fire.

3.) Wolves are assassins. They will jump to the furthest unit available. Put a brawler, knight, guardian, or kassadin in one of the back corners, and then put everyone else a few spaces away from that. The wolves will jump to the tanky member, and the rest of your team is free to destroy them unharmed. Wolves are extremely squishy. I've taken out the entire wolf round with a single 1-star aatrox ability.

I don't die to minion rounds ever anymore. Maybe I did in like my first ever games of TFT when it launched - but I quickly learned not to.