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Datamined Puzzle mode names/bosses
It seems that in the datamined card data, there's cards that act to start the various lethal puzzles. From this, we can get the names of the puzzles. According to this, there are actually 4 different kinds of puzzles, 123 in total.
Source of data: https://hearthstonejson.com/
Lethal Puzzles
These puzzles are described as "Destroy the enemy hero."
Puzzle Puzzle Name Lethal Puzzle 1-1 Cold Blooded Lethal Puzzle 1-2 Frostbite Lethal Puzzle 1-3 Battle Boar Lethal Puzzle 1-4 Stand By Me Lethal Puzzle 1-5 Frothing Fighters Lethal Puzzle 1-6 Leeroy Returns Lethal Puzzle 1-7 Cosmic Fire Lethal Puzzle 1-8 Full Draw Lethal Puzzle 1-9 Plan B Lethal Puzzle 2-1 Quick and Quiet Lethal Puzzle 2-2 Dinosaur Domination Lethal Puzzle 2-3 Hot Potato Lethal Puzzle 2-4 A Dim Flame Lethal Puzzle 2-5 Lethal Lepers Lethal Puzzle 2-6 The Wall Lethal Puzzle 2-7 Four Horsemen Lethal Puzzle 3-1 Light and Fire Lethal Puzzle 3-2 Hostile Hoppers Lethal Puzzle 3-3 A Corrupted Spirit Lethal Puzzle 3-4 The Best Offense Lethal Puzzle 3-5 Healing Hammers Lethal Puzzle 3-6 Toasted Hydra Lethal Puzzle 3-7 C'Thun! C'Thun! C'THUN! Lethal Puzzle 4-1 Tossing Taters Lethal Puzzle 4-2 Pride's Fall Lethal Puzzle 4-3 Keepers of the Gate Lethal Puzzle 4-4 A Shaman's Strength Lethal Puzzle 4-5 Selective Stampede Lethal Puzzle 4-6 Spell Addiction Lethal Puzzle B-1 Of Pirates and Patrons Lethal Puzzle B-2 Erratic Explosive Lethal Puzzle B-3 Never Go Full Northshire Lethal Puzzle B-4 Full Northshire Board Clear Puzzles
These puzzles are described as "Clear the battlefield of all minions."
Puzzle Puzzle Name Board Clear Puzzle 1-1 Quick Attack Board Clear Puzzle 1-2 Holy Extermination Board Clear Puzzle 1-3 Stomp the Snail Board Clear Puzzle 1-4 Sticky Scarecrows Board Clear Puzzle 1-5 The Power of Pigs Board Clear Puzzle 1-6 Position Perfection Board Clear Puzzle 1-7 Scorched Earth Board Clear Puzzle 1-8 Dragon Removal Service Board Clear Puzzle 2-1 Fighter's Finale Board Clear Puzzle 2-2 No More N'Zoth Board Clear Puzzle 2-3 Contamination! Board Clear Puzzle 2-4 A Stolen Shadow Board Clear Puzzle 2-5 Hurricane of Horrors Board Clear Puzzle 2-6 Curious Crustacean Board Clear Puzzle 2-7 Shocking Spells Board Clear Puzzle 3-1 Tiny Terrors Board Clear Puzzle 3-2 Defiling Demons Board Clear Puzzle 3-3 A Warrior's Weapons Board Clear Puzzle 3-4 Poultry Provoked Board Clear Puzzle 3-5 Bot Battle Board Clear Puzzle 4-1 Airborne Assault Board Clear Puzzle 4-2 Dog Days Board Clear Puzzle 4-3 Grumble's Rumble Board Clear Puzzle 4-4 Toxic Treants Board Clear Puzzle 4-5 A Dance with Death Board Clear Puzzle B-1 A Storm of Souls Board Clear Puzzle B-2 Plugging Away Board Clear Puzzle B-3 Warlock's Apprentice Board Clear Puzzle B-4 The Test Mirror Puzzles
These puzzles are described as "Match the boss's side of the battlefield exactly."
Puzzle Puzzle Name Mirror Puzzle 1-1 First Steps Mirror Puzzle 1-2 Smoldering Shield Mirror Puzzle 1-3 In a Flash Mirror Puzzle 1-4 Adorable Sacrifice Mirror Puzzle 1-5 Pursuit of Knowledge Mirror Puzzle 1-6 Brazed Pork Mirror Puzzle 1-7 Shields Up! Mirror Puzzle 1-8 Three Odd Yetis Mirror Puzzle 2-1 Loss and Gain Mirror Puzzle 2-2 Explosive Assault Mirror Puzzle 2-3 Dragonslayer Mirror Puzzle 2-4 Nature's Wispers Mirror Puzzle 2-5 Burning Volley Mirror Puzzle 2-6 Divine Alignment Mirror Puzzle 2-7 Aha! Mirror Puzzle 3-1 The Ol' Switcheroo Mirror Puzzle 3-2 It's in the Stars Mirror Puzzle 3-3 Nether Side Up Mirror Puzzle 3-4 Filthy Rodent Mirror Puzzle 3-5 A Quest for Three Mirror Puzzle 3-6 Chilling Winds Mirror Puzzle 4-1 Noble Sacrifices Mirror Puzzle 4-2 Shrinking Solutions Mirror Puzzle 4-3 Perfect Patrons Mirror Puzzle 4-4 Deathwing Dilemma Mirror Puzzle 4-5 Infestation! Mirror Puzzle B-1 Cruel Souls Mirror Puzzle B-2 Ride the Wave Mirror Puzzle B-3 Hello Darkness Mirror Puzzle B-4 The Ray of Roasting Survival Puzzles
These puzzles are described as "Survive the boss's Hero Power."
Puzzle Puzzle Name Survival Puzzle 1-1 Don't Panic Survival Puzzle 1-2 A Gentle Touch Survival Puzzle 1-3 Cleansing Corruption Survival Puzzle 1-4 A Dire Situation Survival Puzzle 1-5 Double Dip Survival Puzzle 1-6 A Priest's Feast Survival Puzzle 1-7 Splash! Survival Puzzle 1-8 Visions of Vitality Survival Puzzle 2-1 Up for Auction Survival Puzzle 2-2 Sowing Seeds Survival Puzzle 2-3 Mechanical Medic Survival Puzzle 2-4 Lifesteel Survival Puzzle 2-5 Double Trouble Survival Puzzle 2-6 Revived and Refreshed Survival Puzzle 3-1 That's the Spirit Survival Puzzle 3-2 Underhanded Dealing Survival Puzzle 3-3 Pesky Priest Survival Puzzle 3-4 Hallazeal? Hallaheal Survival Puzzle 3-5 Primal Investment Survival Puzzle 3-6 Healing Hands Survival Puzzle 4-1 Just Jaraxxus Survival Puzzle 4-2 Strike Me Down Survival Puzzle 4-3 For Me? Survival Puzzle 4-4 Risky Research Survival Puzzle 4-5 Tempting Demons Survival Puzzle B-1 Mal'Ganis and Me Survival Puzzle B-2 Sharing is Caring Survival Puzzle B-3 The Path to Victory Survival Puzzle B-4 Doomed! Survival Puzzle B-5 Copycats Survival Puzzle B-6 Fungal Frugality Bosses
These heroes appear to be the bosses for puzzle mode.
Some of these don't seem to have associated hero powers. They might share them with another boss, or possibly actually be the player heroes, so their hero power would be one of the basic hero powers. I don't know.
Boss Hero Power Name Hero Power Text Test Subject (None/Unknown) Astromancer Arwyn (None/Unknown) Stargazer Luna Duality There's symmetry in the stars. Zerek, Master Cloner Perfection Everything must be perfect. Dexter the Dendrologist (None/Unknown) Flobbidinous Floop Gloop Sprayer The most effective fertilizer this side of Outland. Demonologist Draan (None/Unknown) Dr. Morrigan Soul Battery Stores souls... for science. Poisonmaster Pollark (None/Unknown) Lil' Stormy (None/Unknown) Electra Stormsurge Stormsurge These puzzles are elementary. Myra Rotspring Experimental Necrium Good poisons work instantly. Boomnician Breena Firework Volley Heal to full to survive this experiment! Boommaster Flark Firework Barrage Heal to full to survive this experiment! Glow-Tron 2000 Glowing Laser Heal to full to survive this experiment! Crystalsmith Kangor Radiant Laser Heal to full to survive this experiment! Dr. Boom True Perfection Have you ever seen such a magnificent reflection? Dr. Boom Fusion Core Why stop at souls? Dr. Boom Kadoom Bot The fuse is lit. Dr. Boom Death Ray Deal 40 damage to the enemy hero.
Mike Donais
Keep trying until you get lucky is not a feature of the puzzles. They are all solvable on the first try.