This was the setup that finally worked for me. The “supporting cards/potions” section is more my opinion, because I did not actually have those cards in my successful run but I was looking for them the whole time.
Relics:
Sling of Courage - Start each Elite combat with 2 Strength.
Gambling Chip - Very useful for reshuffling your opening hand so you can get as many Strength-related cards as possible. Of course, you still need enough energy to actually play them.
War Paint - Useful if you get Strength-related Skill cards very early in the game, because it can upgrade them for free.
Cards:
Armaments+ (upgrade ASAP) - Gain 5 Block. Upgrade all cards in your hand for the rest of combat. This is useful for upgrading as many Strength-related cards in your hand as possible. When paired with Bottled Lightning and Gambling Chip, it can ensure that you’ll always have the best Strength-related opening hand.
Inflame+ - Gain 3 Strength.
Limit Break+ (upgrade ASAP) - Double your Strength. This should be upgraded as soon as possible so it no longer Exhausts. Alternatively, if you can obtain it, Strange Spoon relic can sometimes help with the unupgraded version.
Most important cards:
Limit Break and Inflame are the most important cards for this achievement.
With Limit Break+, you can keep doubling your Strength:
2 Strength -> 4 -> 8 -> 16 -> 32 -> 64
3 Strength -> 6 -> 12 -> 24 -> 48 -> 96
4 Strength -> 8 -> 16 -> 32 -> 64
So even a tiny amount of Strength is enough if you can play Limit Break+ repeatedly.
I managed to earn the achievement against the Shelled Parasite on the first floor after beating the Act 1 boss, with Ironclad on Ascension 0. I had 19 cards in my deck (2 Inflame+ cards), and the combat ended with 58 Strength.
The surprise golden thing I really didn’t expect to be so useful was the Gambling Chip. You can also use Gambler’s Brew to try to get Inflame, Limit Break, and other useful setup cards into your opening hand.
Supporting cards:
Flex+ - Gain 4 Strength. At the end of your turn, lose 4 Strength.
Spot Weakness+ - If the enemy intends to attack, gain 4 Strength.
Demon Form - At the end of your turn, gain 2 Strength. However, since it costs 3 energy, it is a risky card to rely on.
Supportin potions:
Strength Potion - Gain 2 Strength.
Flex Potion - Gain 5 Strength. At the end of your turn, lose 5 Strength.
Cultist Potion - Gain 1 Ritual. At the end of your turn, gain 1 Strength.
Supporting relics:
Vajra - At the start of each combat, gain 1 Strength.
Girya - You can now gain Strength at Rest Sites, up to 3 times.
Red Skull (riskier) - While your HP is at or below 50%, you have 3 additional Strength.
Sacred Bark - Doubles the effectiveness of potions. This means, for example, that Strength Potion gives 4 Strength instead of 2, and Flex Potion gives 10 Strength instead of 5.
Note: I also tried the route of gaining Strength from losing health through cards, specifically with this combo: Rupture + Bloodletting, Brutality, Offering, Combust, Hemokinesis, and Immolate. But it never worked out because the enemy died early or I couldn’t stay alive long enough to gain the needed 50 Strength during combat.