Also, spending is done from the closest town you own... you can't always help where you spend from when buying something like a castle, but you can always place a footman on a territory you control from the town you want the $ to come from. This is key on a map like backstabbed, where you have 6 towns in close proximity.
Outside of the basics, one major strategic aspect of achieving the fastest time is figuring out where bandit camps will be placed and how bandit money will be distributed. Bandit camps can only go on neutral, uncolored territory. If there are no neutral territories, new bandit camps cannot form... so it may be best not to claim a spot sometimes so you can harvest the "taxes" from the bandits on the map.
I wish it recorded fastest completion time for each level so I'd know if it was possible to complete something faster or not. Like Inside a House seems like it shouldn't be that bad but my best time is 20. Anyone faster than 22 for Hex or 27 for Locked In?
As others had mentioned, Towerfall is a pain. I did manage to beat it in 28 turns on hard though. The key is to induce at least a partial collapse of grey via zombies. I managed to do so a lot faster than others since I controlled the entire upper region fairly early. I put a tower at the bottom of my town which both secured those spots from grey and forced more of a zombie buildup along grey's northern border. It collapsed a couple of additional grey cities, which prevented it from gaining enough power to kill the other little guys... then I used a knight to push down and gain more and more space, making sure not to directly cut off any towers right next to the knight (as they'd become zombie towns if I did).
unfortunately the timer randomly resets sometimes when saving and reloading (although very, very rarely, I've seen it 2-3 times out of thousands of saves and reloads). I finally got a legitimate time of ~6:30 but it shows my best time as under 3 minutes.
After a ton of suicidal playthroughs, I got a legit 8:35 time with the rogue (fortunate enough to drop through floor on the 16th within blinking distance of goblet)... basically swiftness with hellfire and heavily upgraded charm of blinking and a lot of luck. Any legit times better than that?
If the creator wanted to go the whole gay love route, fine. Was it really necessary to have the "dear this" and "honey that" bits, for people who BARELY KNOW ONE ANOTHER? The whole series is well put together, but I can't even finish this segment because the love is so contrived and in my face.
To get the impossible badge, you need at least 5 cantrips and 5 shields... Don't bother going to gauntlet lvl 1 with less than that. There are a lot of RNG factors on top of that, such as: what's offered at the end of each level, how many coins you get from the coin packs (3-5), the cost of what's offered (shield 5-6, cantrip 10-12), and the blight distribution on the final level. If the blight is evenly distributed, you have no shot... you need at least a few squares with 2 or less blight.
Priffadas is mostly correct, but there are a couple of things he didn't mention that I want to bring up. First, the amount of coins you get from those coin sacks is random, anywhere between 3-5, so if you want the impossible badge, it's just as important to have good luck with those as it is to finish the level in the minimum turns possible. Second, purchase costs also vary for shields and cantrips. Shields can be 5 or 6 coins, cantrips 10-12 coins. Don't pay max cost unless you're 100% forced. Even with all of that, you may still lose. Last time, I had 6 shields and 6 cantrips, hadn't taken any damage, and STILL died on gauntlet lvl 7 due to a bad draw order.
I've made it to guantlet lv 7 with 4 hearts twice. Both times I died before turn 3. I'm not sure what to do when 80% of the spaces have 4+ blight on them...