Sounds like you haven't cleared the 3rd boss yet, so I'll try to avoid spoiling anything past that.
First off, boss gimmicks.
For the prospector, the goal is to kill the pack mule during the first phase so you have a truckload of cards to use in the second. If possible, you want some empty spaces on your side of the board when the first phase ends so you can immediately start playing things.
The angler is the one that spooks me the most, since the second phase can get out of control fast. Ideally, you want a high cost, powerful card in your hand when the first phase ends. He'll slot in bait buckets across from your existing cards, so you want to sacrifice all of them to drop a huge fatty and kill him before he gets a chance to do anything. During the first phase, make sure you're drawing Squirrels on the turns where he threatens to hook things (unless he's trying to hook a near-dead creature, then it might be best to let him).
I think they trapper may be the easiest once you understand his gimmick. The goal is to suicide cards into all 4 traps, but to do so slowly (otherwise he'll often just kill you before you restock). If you've upgraded Squirrels to Bees, they can be used to set off traps, which is really helpful for preserving your stronger cards. If you set off all 4 traps, you'll have 5 pelts to trade during the second phase, and it should be smooth sailing from there.
Other tips:
Try to avoid spending items until you hit your first backpack event so you can get a free pack rat. In addition to being pretty useful, pack rats are also a rare, and for reasons you may not have seen yet, having a lot of rares in your deck will pay off later.
Once you have the squirrel head wood carving (or the insect head, if you've upgraded to bees), meeting the wood carver and looking for body carvings is a great idea. While not everything you'll find is good, certain sigils are absolutely busted when applied to squirrels/bees. Things like undying, triple blood, the sigil that grants a worker ant on play. Get a good one and you can win the run right there.
During the early fights, never accept a peace branch and always focus on getting as much overkill as you can. Getting a stash of teeth early makes visiting the trapper very rewarding, since cashing in 2-3 golden pelts will make your deck way stronger. Only ever buy golden pelts though. The hare and wolf pelts are just going to lead to a more clogged deck.
Unless you get a way to generate lots of bones easily, you typically want only a couple of bone based creatures, but you do want some. They can help generate momentum in tight spots when you don't have much to sacrifice.
Mantis God is insane. If you can increase one's attack power at a camp fire, you can steal fights left and right, since a 2-attack Mantis God will deal 6 damage on turn one. It's strong in boss fights too.
Certain rares are much stronger in the early game, like Ouroboros and Geck. If you see these near the start, take them (unless it's a choice between them and a Mantis God). Late game, you can probably pass on them.
Some fights can run long enough to make you run out of cards if your deck is too slim, so trying to keep deck size as small as possible isn't a great strategy. That means you also can't really rely on just one super-card to win, so try to make sure you're not putting all your eggs in one basket. (This is why a woodcarving that buffs squirrels/bees is so strong. It's consistent.)
This last tip I didn't even figure out during my playthrough, and it seems way busted. But if you're really stuck, maybe it could help. Apparently, if you visit a campfire and repeatedly send up a poisonous creature, like an adder, then when it gets eaten, it'll kill all the people around the campfire. Apparently this lets you use all future campfires 5x each with no risk of losing your creature. Seems nutty when applied to stuff like Mantis God.