Like Rebuild Homeland quest in Al De Baran, Black Hole's Threat quest cannot be completed in a single day. This quest required you to complete Black Hole tasks and you need to collect 20 Time Shards. This shards can be obtained by clearing sub quests in Al De Baran. Sub quest resets everyday. Talk to Jocelyn, Cecelia, Carol and Cindy NPCs around Clock Tower entrance.
You can only get 4 Time Shards per day. Once completed, Go to Mosman Time to submit the Time Shards and he will reward you with Base, Job Experienc, Clock *1, LIghtning Chain *1 and Zeny.