Mr Smite
First up is the Tauren Pirate, Mr Smite. His main mechanics are the stealthed minis he spawns in formations around the map, and his secondary weapon set that makes him hard to assault.
On the right hand side we have two mines and a meeting stone. The two mines make this an important lane to contest. The complication is that on the bridge, two Defias Bandits constantly patrol, stunning and killing would-be miners (or fighting minis). The meeting stone is handy to prevent direct assaults on your base, but doesn’t provide easy access to the mines. Often it is best to keep the switch pointing to the left to secure strong control over the mines, and use an unbound to flip the stone when possible.
The left hand side is less of a focus. There’s a single mine with a meeting stone for easy access. It can be easy to forget about it, so try and at least glance over to see if there’s a 3g for the taking. A stealthed Stonehoof Tauren marches down the pipe and attacks your base periodically. It can do quite a bit of damage left alone, and cannot be as easily countered by flying minis, as they won’t unstealth the Tauren. Whelp Eggs are fairly good, or Defias bandits to stun her once she has charged into the base.
Finally we have Smite himself. The main difficulty is when he switches weapons about halfway through his health, dealing an AoE stun + knockback. This makes using melee minis against him quite hard, and even ranged minis can be caught in it. If you come with unbound tanks, like Quilboar or Earth Elemental, they can be placed near the door in the picture above. This prevents them from being thrown back too far.
Overall, Mr Smite is a challenging but not mechanically complex encounter. He throws waves of minis at you fairly aggressively and securing the gold can be frustrating at times, but otherwise presents a straightforward fight.
Cookie
Cookie the cook is in one sense a very simple fight. It asks one question - can you AoE down the waves of upgraded minis she sends at you? If not, you lose.
Clearing the entire pack (especially with bonus levels) can be quite hard. What is simpler is first dropping a spell or S.A.F.E Pilot to clear the Mountaineers and Darkspear Troll, followed by a Flying Mini to wipe out the remaining melee minis.
The rest of the map is not too complicated
Two chests are placed within easy access on the left. These can and should be regularly captured for the bonus gold. The leftmost tower is not so important, but it does make it hard for a miner to take the gold across from it if not secured. Careful positioning is key. Note that ranged minis can fire across the gap.
On the other side we get a wave of Raptors, Prowlers, and Murlocs. The logic is similar, though note that just placing a single Gryphon Rider to clear up the Raptors and Wolves might sacrifice a lot of base hp to the high-dps minis. One thing to note is fairly immediately after the start, the gold mine on the right lane fills up and the AI will usually try to take it. You can beat them to it.
Apart from that, just trying to approach Cookie from two sides is the main remaining tactic. Watch out for the Huntresses, as they can shred the fliers that you might be using to clear the big waves.
Sneed
Last but certainly not least is Sneed. Sneed might seem trivially easy at the lower (green or grey) difficulties, but can become very, very difficult as you climb the levels.
He has a single notable mechanic - his replicator. Once ready (visible by a glowing sparking animation on the platforms), it captures and destroys the next mini that steps onto it. Then, to the right of the bridge, he spawns 6 copies of the mini for himself.
This is immediately demonstrated to you as he initially sends a large wave of goblin sappers at your base. That’s not too bad to deal with. What makes it harder is his army has Ogre Mage, Stonehoof Tauren, and Molten Giants. This means without managing the replicator panels, feeding into it the right minis, you can quickly end up with Oops! All Molten Giants.
There’s a chest left of the base and a mine directly north. Two things to note - if you quickly send a Kobold to the north mine after starting, you usually get that Kobold fed into the replicator. Second, the AI likes to send a Stonehoof Tauren almost immediately to take the left chest. It is possible to dispute it and take it back.
There’s another chest across the bridge and beyond the replicator pad. It can be a tricky one to control without unbound minis. There’s also a reasonably easy mine to control on the right base.
Apart from that, there’s not much else beyond timing when you send your pushes across. The difficulty with Sneed lies in how punishing he is for misplays. If you can keep it up, he falls fairly quickly.
It can be tricky to build an army suitable for all 3 maps. Mr Smite is the least demanding, he only requires a method to handle the Stonehoof Tauren that marches towards your base. Sneed is hard with high-cost minis which limit what can be fed into the machine, but otherwise slightly favours cheap unbound to throw inside. Finally, Cookie places a hard requirement on your army composition. Fortunately, SAFE Pilot is usually sufficient to take out the ranged minis in the push, so there’s a straightforward fix. Since Quilboar is good at tanking Smite in the door, I recommend the trio of SAFE Pilot, Whelp Eggs, and Quilboar as an easy starting base for your Deadmines army.