Optimal Honkai Star Rail Enemy Weakness Coverage

I recently started playing Honkai Star Rail (HSR), a popular turn-based RPG by Mihoyo.

Enemies in HSR have a mechanic known as the “toughness bar”. While their toughness is full, enemies receive reduced damage thus we would like to break these bars to our maximize damage. To break enemies' toughness, we would need to damage them with characters that match their elemental weaknesses.

In an ideal world, we would simply have characters of every element to achieve full coverage. However, since HSR is a gacha game, it is impossible to access every character without spending an exorbitant amount of money. This led me to wonder: What is the minimum number of characters needed to cover every elite enemy's weakness? (We're going to ignore non-elites since they can be easily killed without breaking their toughness bar)

To help answer this question, I built this tool to check which enemies are covered by which elements. You can click the element icons in the table header to indicate that you own characters with said elements and the table will automatically update to show which enemies are covered.

Finally, we can use simple brute force to answer our original question: We would need at least four different elements to cover every enemy (as of patch 2.3).

Elite Enemy (0 / 35) Select Weakness
Tomorrow in Harmonious Chords
Present Inebriated in Revelry
Past Confined and Caged
Memory Zone Meme - Shell of Faded Rage
Ten Stonehearts - Aventurine of Stratagems
Dreamjolt Troupe's Beyond Overcooked
Dreamjolt Troupe's Sweet Gorilla
Memory Zone Meme - Something Unto Death
Stellaron Hunter - Sam
Aurumaton Spectral Envoy
Senior Staff - Team Leader
The Swarm - True Sting (Complete)
The Ascended
Abundance Sprite - Malefic Ape
Cloud Knight Lieutenant: Yanqing
Abundant Ebon Deer
Stellaron Hunter: Kafka
Automaton Direwolf
Automaton Grizzly
Blaze Out of Space
Ice Out of Space
Guardian Shadow
Decaying Shadow
Searing Prowler
Frigid Prowler
Silvermane Lieutenant
Voidranger - Trampler
Disciples of Sanctus Medicus - Shape Shifter
Aurumaton Gatekeeper