Hey, I have a little problem.
I have complete the entire campaign in legendary of Halo 5 in my own but i haven’t got the achievements. What can I do? How can I get it?
You service record on Waypoint shows you have completed all levels on Legendary solo. So you’ve met the requirements for sure. Congrats 
Now the issue is Xbox Live. Assuming you still haven’t unlocked it, do a hard reset (hold the power button for like 10 seconds) and play the game again. If that doesn’t work, try waiting a bit for everything to sync up. Lastly, if it still doesn’t unlock, try running through a level on Easy again.