My character is nearly at the end of his career. All I need to do for him is become the ultimate vampire (get all perks), destroy a Legendary Dragon and finally, meet the Ebony Warrior. But at level 78 I've ran into two problems: there are no Legendary Dragons anywhere and I'm struggling to level up to 82. Any ideas where I can find a Legendary Dragon and how to get to Level 82? I'm more of a warrior but I've invested a lot of time into being a mage. I was a stealth build before moving to warrior, so that's still relatively buffed.

Legendary dragons appear at level 75: http://www.uesp.net/wiki/Skyrim:Legendary_Dragon#Legendary_Dragon and the Ebony Warrior at level 80: http://www.uesp.net/wiki/Dragonborn:The_Ebony_Warrior

As for levelling up, I have no idea. Do stuff, by trainings, whatever.

Looks pretty impressive @level 82 !!! Never reached so far.

Only once have I done as you have, long ago.

You must.....(drum roll).........grind!

It is the only way, but I'm sure you've already fully embraced the meaning of tedious in this manner. If you've made it that far, you can reach the end.

Oghma Infinium Glitch, if you can still use it.

Or find a wolf somewhere, taped down the block button, get in a corner and let the wold constantly attack you while blocking. Easy blocks.

Or find an iron sword and hack away at giants until they die to raise one-handed.

Easiest way would be to legendary a skill like conjuration, then soul-trap glitch. Or just legendary illusion/ alteration, then sneak+muffle or detect life in a big city.

For levelling, go Legendary for skills like one-handed/two-handed. They are very easy to rack up again, infinite levelling thus allowing you to hit that magical cap. However, I do suggest you use two of those perks to re-level at the same time, considering you need more levels the higher your level is.

If you seek legendary dragons then fast travel to Riverwood and the College of Winterhold, eventually one will spawn. In my game the strongest dragons for my level always spawn at the College when I FT.