If the next tier of difficulty has not been unlocked in Conquest despite having completed Easy or Normal, there are two possible reasons.

• The current Conquest is still active. If you complete your current conquest with time left over in the event, you will have to wait until the next Conquest event is live before tackling the next difficulty. 

• You did not collect the final Data Disk in your current difficulty. When defeating the final enemies, there is one more reward to collect, which will complete the current difficulty. If you do not collect the final reward, Conquest will not be marked as complete.