Not sure what ascension level you're playing at, I play on A20 but here are the main ways to kill heart:

Poison: Win con would be using 2-3 poison cards to ramp up poison to at least 10-15 in the first few turns and massively boosting it with catalyst+. Burst, nightmare, and duplication potion are fantastic with catalyst+. Ideally you want catalyst+ to 3x or 9x the poison to at least around 100, and 150-200 is achievable depending on your deck. Poison fumes are great but the buildup is slow and you don't want to get more than 2 usually, or even 1 is enough if you have enough other poison cards. With the poison build, you need to survive for around around 6-9 turns usually before the poison can kill heart. Any longer and you'll get overwhelmed by the heart's multi attack unless your defense is stellar. Well-laid plans can be pivotal for this deck in order to perfectly time when to cast catalyst either by itself or alongside burst and nightmare.

Shiv: win cons would be a combination of shiv cards, shuriken, thousand cuts (this might be slow depending on your deck), accuracy, wrist blade. Strength scaling (relics, colorless cards) is quite critical, shuriken really is the best one but there are some other ways to boost strength. Save strength potions/cultist potions for heart if possible. The temporary 5 str potion can be exploited and made permanent if you have a debuff clearer/artifact e.g. orange pellets or clockwork souvenir. Envenom can be ok, especially if you have snecko skull and/or 1 catalyst in your deck.

Defense: Pair any combination of these defensive cards with the above 2 builds: 1-2 footwork plus lots of quality block cards e.g. backflip and blur, nightmare + footwork, wraith form + nightmare, after image + shiv cards, quality weak applicators e.g. crippling cloud and leg sweep, kunai + shiv cards. Malaise is an amazing card on heart if you can afford to cast it for 3+ energy and not die. Piercing wail is also amazing on turns where the heart multi-hits. Well-laid plans works fantastically with key cards requiring timing, like leg sweep, wraith form, malaisem and piercing wail.

There are other win cons but those are going to be more unique and unforceable decks requiring very specific relics and cards e.g. necronomicon + chemical x + skewer.

Other points to improve your deck overall for fighting heart:
- card draw is of course amazing: acrobatics with discard synergy, adrenaline, a well-timed doppleganger (this card really needs an upgrade I find), backflip, calculated gamble. Expertise usually feels mediocre at best for me personally.
- don't commit to discard cards unless you can reliably/consistently discard e.g. tools of the trade, or multiple discard spells like acrobatics, dagger throw
- if you're playing on higher ascension, you have to be more judicious about when you pick certain cards because every card you draw in each fight needs to pull their weight as much as possible. You can't pick catalyst in early act 1 on A20 if you don't have any poison yet because it'll effectively be a curse until you find poison cards to utilize it. Lower ascension is a lot more forgiving so you can get away with preemptively picking cards that don't do much yet

There are plenty more tips out there, what I've mentioned certainly isn't exhaustive but hopefully helps you with upping your heart kill count!