List of quests:

M1☆ -
"Greater Izuchi, Greater Pain" - Hunt a Great Izuchi (Illegal Large Crown)
"Omae Wa Mou Shindeiru" - Slay a Jyuratodus (Illegal Small Crown)

M2☆ -
"Between a Rock and a Hard Place" - Hunt a Barroth and a Basarios
"Mean Green Death Machines" - Hunt a Pukei-Pukei and a Tetranadon
"Cleaning Duty" - Hunt a Barroth and Capture a Royal Ludroth

M3☆ -
"Frosted Fangs" - Hunt a Barioth (Illegal Small Crown)
"Crab Rave" - Hunt 3 Daimyo Hermitaur and a Shogun Ceanataur (Illegal Small Crowns)
"A Shocking Discovery" - Hunt a Zinogre and a Tobi-Kadachi
"Roaring Raptor Rumble" - Hunt a Great Izuchi, Great Baggi and Great Wroggi (Illegal Large Crowns)

M4☆ -
"Little Red and the Big Bad Wolf" - Hunt an Anjanath and a Lunagaron (Illegal Small Crown)
"A Dance of Fire and Ice" - Hunt an Aknosom and an Aurora Somnacanth
"UnBEARable" - Slay an Arzuros and a Goss Harag (Illegal Small Crowns)
"Can We Fix It?" - Hunt a Blood-Orange Bishaten and an Almudron
"Play Time!" - Capture a Khezu and hunt a Magnamalo (Illegal Small and Large Crowns)

M5☆ -
"Spider Infestation" - Hunt a Rakna-Kadaki and a Pyre Rakna-Kadaki (Illegal Small Crowns)
"Power, Wisdom, Courage" - Hunt a Tigrex, Aurora Somnacanth and Zinogre
"Gone But Not Forgotten" - Hunt a Mizutsune and an Astalos
"Blade and Muscle" - Hunt a Seregios and a Rajang
"Pinecone Panic" - Hunt a Blood-Orange Bishaten, Seregios and Bazelgeuse

M6☆ -
"No More Monkeys Jumping on the Bed" - Capture a Bishaten and a Rajang
"Deviant Disaster" - Slay the Apexes of Arzuros, Mizutsune, Rathian, Rathalos and Zinogre
"Chaotic Rage" - Hunt a Gore Magala (Illegal Large Crown)
"Advanced: All That Glitters is Gold" - Hunt a Furious Rajang and a Gold Rathian
"Advanced: Assassination Attempt" - Slay a Chameleos and hunt a Lucent Nargacuga
"Advanced: Bombing Run" - Slay a Teostra and hunt a Seething Bazelgeuse
"Advanced: Shimmering Firestorm" - Slay a Kushala Daora and hunt a Silver Rathalos
"Advanced: A New Frontier" - Hunt a Flaming Espinas and a Lucent Nargacuga
"Advanced: Samurai Showdown" - Hunt a Magnamalo and a Scorned Magnamalo
"Advanced: Shooting Stars" - Slay 3 Crimson Glow Valstrax (Illegal Small Crown)
"Advanced: Spookier Citadel!?" - Slay an Afflicted Garangolm, afflicted Lunagaron and Malzeno
"Advanced: Season's Breedings!" - Slay Wind Serpent Ibushi and Thunder Serpent Narwa

M6☆ Special -
"RAGNAROK: Sun's Shadow" - Hunt a Silver Rathalos and a Gore Magala
"RAGNAROK: Ring of Fire" - Hunt a Flaming Espinas and a Lucent Nargacuga
"RAGNAROK: Approaching Thunderstorm" - Hunt an Astalos and slay an Apex Zinogre
"RAGNAROK: Gift of the Gods" - Hunt a Violet Mizutsune and slay a Shagaru Magala
"RAGNAROK: A True God's Wrath" - Slay Wind Serpent Ibushi
"RAGNAROK: Archonic Rage" - Slay an Aurora Somnacanth (Illegal Large Crown)
"RAGNAROK: Severed Dreams" - Hunt a Goss Harag (Illegal Large Crown)
"RAGNAROK: Demon's Folly" - Slay an Afflicted Lunagaron and a Malzeno (Illegal Large Crown)
"RAGNAROK: Into Despair" - Slay Gaismagorm (See Bold Note Below)

M1☆ Small Monsters -
"Bombadgy Bowling" - Slay 15 Bombadgy or Bullfango
"Catastrophe" - Slay 15 Felyne or Melynx
"Oh No!" - Slay 12 Popo or Anteka
"Culling The Weak" - Slay 12 Zamite
"Quest For The Golden Egg" - Slay 5 Gargwa and deliver a Gold Gargwa Egg
"Passive Aggression" - Slay 12 Slagtoth or Rhenoplos
"Desert Destroyers" - Slay 13 Kestodon or Delex
"Pest Control" - Slay 10 Altaroth or Bnahabra
"Immortal" - 'Slay' 10 Kelbi
"Jungle Fever" - Slay 12 Velociprey or Vespoid

M6☆ Triple Threats -
"Triple Threat: Beastly Essence" - Hunt an Arzuros, a Lagombi and a Volvidon
"Triple Threat: Burning Skies" - Hunt a Rathalos, a Silver Rathalos and an Apex Rathalos
"Triple Threat: Venomous Earth" - Hunt a Rathian, a Gold Rathian and an Apex Rathian
"Triple Threat: Scrambled Eggs" - Hunt 3 Seething Bazelgeuse
"Triple Threat: Too Much" - Hunt 3 Furious Rajang
"Triple Threat: Afflicted Nightmare" - Hunt a Scorned Magnamalo, Furious Rajang and Gore Magala all afflicted
"Triple Threat: Elder Trio Trial" - Hunt a Chameleos, a Kushala Daora and a Teostra
"Triple Threat: Risen Trio Trial" - Hunt a Risen Chameleos, a Risen Kushala Daora and a Risen Teostra
"Triple Threat: Chaos Incarnate" - Hunt a Gore Magala, a Shagaru Magala and a Chaotic Gore Magala
"Triple Threat: Wind God's Requiem" - Hunt 3 Wind Serpent Ibushi
"Triple Threat: Thunder Goddess' Revenge" - Hunt 3 Thunder Serpent Narwa


Notes:
-Some quests have special monsters in them. (You'll know when you encounter them)
-The M6☆ quest "Deviant Disaster" excludes Apex Diablos due to the fact that it simply stands there and does nothing once engaging the player.
-The M6☆ quest "Advanced: All That Glitters is Gold" was made before I realized a Furious Rajang/Gold Rathian quest existed normally. oops
-Capture quests don't have EZ Traps in the supply box. I haven't found the right item box ID for Master Rank capture quests yet.
-The Special Quest "RAGNAROK: Into Despair" replaces the normal Giasmagorm quest that unlocks after beating it in the story due to cutscene triggers being specific to the quest ID.