To access Asmodeus raid and dungeons you have to clear Mist quests first.
Go to Hunter's Night and talk to your <Hub Transport> NPC.
Accept a normal mission called "7th-type Encounter".
Click spoiler below to see Mist quests progression:
After you finished all Mist quests
go to Fantasy World: Dream Theater <<Reverse>> and talk to <Count D>.
Accept a main mission called "A foretold invitation".
Click spoiler below to see Asmodeus quests progression:
After finishing the quests you should have access to all of Asmodeus dungeons and raid.