You can do these particular quests ONLY ONCE each, though you can join people posting the quest even if you have already completed the quest yourself. A few of these Special Assignments acts as gates in a quest line, opening up the next one in sequence. The others are either the final quest in the line or a standalone quest that unlocks the full fight with the new monster. This is what you are ultimately after, because completing these quests will unlock a somewhat equivalent Optional Quest that you fight this new monster in, and that quest is repeatable indefinitely for farming and glory!
NB: Special Assignments are not available in High Rank when you're with the Serious Handler during the Iceborne story progression.
|★7||The Food Chain Dominator||Hunt a Deviljho||14400|
|★8||The Blazing Sun||Slay Teostra||18000|
|★8||Pandora's Arena||Repel Lunastra||12600|
|★8||No Remorse, No Surrender||Slay Lunastra + Teostra||28800|
|★6||A Visitor from Another World||Slay Kulu-Ya-Ku||10800|
|★9||The Legendary Beast||Repel Behemoth||17640|
|★9||He Taketh It With His Eyes||Slay Behemoth||25200|
|★9||Contract: Trouble in the Ancient Forest||Slay Leshen||19800|
Master Rank Special Assignments (Iceborne Expansion)
Master Rank Special Assignments are available in Monster Hunter World: Iceborne from October 10th 2019, with Patch 11.01. Players can find Purple exclamation marks in Seliana to begin special assignments. The first one is Sterling Pride, given to you by the Admiral in Seliana.
|6||Sterling Pride||Slay a Kirin||36000|
|6||Reveal Thyself, Destroyer||Hunt a Rajang||36000|
|6||Across the Lost Path||Hunt a Stygian Zinogre||36000|
|6||Point of No Return||Repel Safi'jiiva||36000|
|6||...And My Rage for All||Slay a Raging Brachydios||43200|
|6||The Fury Remains||Hunt a Furious Rajang||43200|
|6||Blazing Black Twilight||Slay an Alatreon||43200|
|6||Dawn's Triumph||Slay an Alatreon||28800|
|6||The Black Dragon||Slay Fatalis||57600|