This is a bit more difficult to answer because there are a lot more things that factor into higher-level play, but I'll still give a few unassorted tips that come to mind.
Watch expert players
For example, jorbs is one of the best Slay the Spire players if not the best and I learned a lot from watching him play. There are all sorts of combos and interactions that you would never think of until you see a pro player pull it out of their bag of tricks.
This is probably the most important tip out of all them, so if there's only one tip you take away from the post it should be this one. This is how I learned a lot of my intermediate/advanced tricks.
Cover all the basics
In order for your deck to do well against most fights you'll want to minimally strengthen it in all of these areas:
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short-term damage
For example, like Immolate, which does a lot of damage up front but would be nowhere near enough damage to take out the Corrupt Heart.
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long-term ("scaling") damage
For example, like Limit Break+, which you can keep casting to eventually do a massive amount of damage, but it takes longer for that damage to come online.
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short-term block
For example, like Impervious, which does a lot of block up front, but provides no benefit after that.
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long-term ("scaling") block
For example, like Feel no Pain, which can generate a LOT of block over the course of a fight, but perhaps not a lot of block on the turn you play it.
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short-term card draw
For example, like Offering, which gives you a burst of card draw at the beginning of the fight, but then no benefit after that.
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long-term ("scaling") card draw
For example, like Brutality, which generates a lot of card draw over the course of a fight, but not on the turn you play it.
There are other things you may also want to cover (like damaging multiple enemies, being resistant to statuses), but the above areas are, like, deck building 101.
Card draw and card quality are really important
The most common reason a deck dies is because it drew the wrong hand at the wrong time. It's much better to spend the right three energy than the wrong four energy.
In fact, you should view most boss relics as essentially vehicles for improving card draw or card quality. In particular, if you take a boss relic that increases your energy by one per turn then you want to be spending that extra energy on cards that draw at least two more cards like Pommel strike+, Coolheaded, or Backflip.
For example, Snecko Eye might seem like a trash relic to an inexperienced player, but it's actually really strong if you can stomach the penalty because drawing two extra cards per turn is absurdly good. In fact, it's such a strong path to victory that you'll see some players deliberately skew towards more expensive cards in Act 1 just for the chance of getting a free win if they're offered Snecko Eye for the Act 1 Boss relic.
For similar reasons, in the Donu and Deca fight, it's Deca that's the more dangerous of the two, because every two Dazes that Deca adds to the deck are two wasted card draws.
Abuse relics whose countdowns carryover between fights
Specifically, I'm talking about the following relics:
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Every 10th Attack you play deals double damage.
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Happy Flower - Every 3 turns, gain 1 Energy.
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Nunchaku - Every time you play 10 Attacks, gain 1 Energy.
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Ink Bottle - Whenever you play 10 cards, draw 1 card.
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Incense burner - Every 6 turns, gain 1 Intangible.
For example, you might look at Pen Nib and think: "Oh, this doubles one out of every 10 attacks, so on average that makes me do 10% more damage, right?" WRONG. If you can safely delay the end of a fight you want to try to rack up more charges on Pen Nib using smaller attacks so that its countdown is around 8 or 9 by the end of the fight. That way the first or second attack of the next fight gets doubled. This trick will increase your meaningful damage output by much more than 10% since the first few attacks of a fight are much more valuable than the trailing attacks that you squeeze in at the end of a fight to charge it back up.
Similarly:
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You usually want to end a fight with the countdown for Happy Flower on 2
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You usually want to end a fight with the countdown for Pen Nib, Nunchaku, or Ink Bottle on 9
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You usually want to end a fight with the countdown for Incense Burner on 4 or 5
The exact number to end on depends on what fights are coming up. For example, if you're fighting the Spire Shield and Spire Spear then you want the Incense Burner's countdown to be on 4 at the end of the fight and definitely not 5 (otherwise it will always trigger on turns that the Corrupt Heart doesn't attack on).
Debuff cancellation/removal is stronger than you think
Debuff cancellation/removal comes in the form of either Artifact charges or Orange Pellets and is incredibly strong in a lot of ways.
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cancelling the debuff from Speed Potion or Flex Potion makes them last the whole fight
This is one of the first tricks I learned from watching Jorbs play!
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cancelling the debuff from Flex makes it last the whole fight
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cancelling the debuff from Mutagenic Strength makes it last the whole fight
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canceling the debuff from Wraith Form makes it way stronger
In particular, Wraith Form combos really well with Orange Pellets (since it's a Power!).
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canceling the debuff from Biased Cognition makes it way stronger
Biased Cognition also goes extremely well with Orange Pellets (since it's also a Power!).
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removing the debuff from Snecko Eye gives you two free card draw per turn!
This only works with Orange Pellets and it will still randomize the energy costs of your starting hand.
In fact, this is a good point to mention that Orange Pellets in particular is very very strong even if you don't combo it with anything else. It's probably one of the strongest shop relics if not the strongest. For example, in the Corrupt Heart fight you can use Orange Pellets to remove all three of the starting debuffs, which is very very very good.
The Ascension 20 penalty separates the women from the girls
I remember when I was grinding Ascension levels for the Defect I sailed through Ascension levels 10-19 after learning various intermediate tricks and then spent waaaaaay too long figuring out how to beat Ascension 20.
There are a few reasons why the Ascension 20 penalty (an extra boss for Act 3) is particularly devastating:
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It really exercises your potion management skills
Carefully stewarding and using potions is an extremely important skill to win the game on Ascension 20 because of the sequence of four hard fights almost in a row: the two Act 3 boss fights, the Act 4 elite fight, and the Act 4 boss fight. On Ascension 20 you only have two potion slots and you have very very carefully think through which of those four fights you will use those two potions on.
You will get an opportunity to purchase a few more potions from the Act 4 merchant, but you can't rely on those potions being that useful or relevant. The two potions that you bring with you to the end of Act 3 will tend to be far more important and impactful to your chances of winning because you can (and should) tailor the potions you hold onto in order to address those final four hard fights.
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The second boss fight is less predictable
For the first Act 3 boss fight you can see in advance which boss you're fighting at the beginning of Act 3, but you don't know for sure which one will be the other boss, so you can't prepare as easily for that second fight.
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RNG won't save you
Your deck might be particularly weak against one of the three possible Act 3 boss fights and before Ascension 20 you have a 2/3 chance (a decent chance!) to avoid the fight you're weak against and when that chance drops to 1/3 you're forced to build a more versatile deck instead of building a one-dimensional deck and crossing your fingers that you random the boss you want.
This particularly true for the Defect, because he tends to be more Power heavy than the other characters and one of the three Act 3 Boss fights (the Awakened One) punishes Power-heavy decks. This is a big reason why I struggled so hard to clear Ascension 20 with him (I had to learn how to win with him without leaning on Power cards so much).
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It stresses the run at an already weak point
You don't get any rewards for beating the first Act 3 boss fight and then you're immediately plunged into another boss fight without a chance to heal or anything (and you also don't get any rewards for beating that, either
).
Think about likely upcoming fights
When in doubt about what card or relic to pick, think through the possible upcoming fights (especially Elite fights). Ask yourself how you think your deck fares against each possible fight. Do you notice any fights that you think you will be weak against? Do any of the cards or relics that you're being offered help you shore up those weaknesses?
Push your luck a bit at the end of each act
Since you heal up most of your health at the end of each act, you ideally want to be a little bit greedy at the end of each act if you think you can get away with it because any health you spend to save a potion or to obtain a relic or take one more fight will (mostly) heal right back up at the beginning of the next act.
Every 1 HP matters
Details matter when you play on the highest difficulty level. A lot of Ascension 20 runs fail due to off-by-one errors where 1 HP would have made the difference. If you think you can save 1 HP by overthinking a particular turn, then break out the calculator or spreadsheet and overthink that turn.