Could you advise me how to beat The Blood of Gondor scenario in solo play?

I tried mono tactics deck /Beregond, Legolas, Boromir/ through siege, but in most cases I don't have the required number of defenders when enemies show up from the hidden cards.

What deck can handle it with high win ratio?

I haven't played against this quest in a while but the deck I used at the time was a location control deck with Elrond/Spiritfindel/Denethor.

Elrond and Denethor have decent defence to start off the quest, not to mention it helps you know what cards are coming up or figuring out what hidden cards go into your staging area. Henamarth helps with this too. Knowing what hidden cards you have make guessing with Faramir that much easier.

Spiritfindel brings along Asfaloth which really helps on a lot of the locations that give you hidden cards. Asfaloth can also immediately cure the need of putting up with siege if you get him first turn. Vilya with Elrond to play some Northern trackers and use them to clear all the locations up. Use burning brand on either Gildor or Elrond to stop the deadly shadows from coming in. The highest attack enemy in the encounter is 4 or something so either of those defenders will take only 1 damage. This could be remedied easily by having Arwen in the deck or Warden of healing, or both!

With a good set up you can gain board control during part 1 then part 2 should be a breeze. Since you can get a lot of allies out quite quickly with Vilya and save Gandalf for when part 2 begins. Alternatively you could have Gandalf from OHaUH since with this set of heroes you can easily play with 2-3 Gift's of the Galadhrim and 3 Council of Elronds. This keeps your threat low to pay for the Gandalf later in the game.

The above advice is sound. My Elrond/Spirifindel/Mirlonde deck absolutely laughs at BoG. It starts with low threat and can keep it low easily. You build up an army of powerful elves and then take on the first boss and win in three turns after.