Balerion Trial Deck

My immediate thought is, 70 cards makes it one fat deck!!

Is this deck going to be for Joust, Melee or both? I ask because four of your plots give your opponent something as well as you, which won't always be in your interested. Spending the Winter Stores is the safest, as rarely will their in-house attachment be a massive risk to you, assuming they have any in their deck at all.
I am intrigued as to why Focused Offense is in the deck, as only doing one claim 3 challenge that you can then not defend (and may not go first with) is risky. Whereas a claim 2 plot that does allow you to defend and do more than one challenge may benefit you more.

For your characters, as Old Bear Mormont will need to die at some point to protect you from a plot, where the second copy? If he is killed off before seeing the second copy, you have a dead card. And if you use it as a duplicate, it will still be wasted when you use his ability to negate a plot.
I think that using the shadow Hatchlings to get even more duplicates is excessive, but you may have a meta where that many duplicates are needed to keep your dragons alive.

As I imagine you will be sacrificing Intrigue challenges for Heir to the Iron Throne, will Qarth give you much? You have other characters who can defend Intrigue, and Deadly won't really add much as few things will be able to cope with the Stealth, and would only make the challenge opposed and stop you getting an extra power. Also, even if you intend to Ambush everything that you can, the only income bonus you have is a single Tent. You do have reducers, but they won't help you get out Old Bear Mormont who will eat up all of your gold for the turn, assuming you flipped a 4 gold plot and also had the Tent out previously.

I would drop Blood of the Dragon. As you aren't a Dragon until after you declare attackers, the character will be kneeling and so won't be able to benefit from Daenerys's ablity. Add in more Dragon Lore, as it gives you redundancy, and means you have the option to get out more than one Dragon a turn. Or you could look for something else with Spending the Winter Stores.

Citadel Custom is a nice addition, although would be best with a claim 2 plot. But a single Forever Burning won't do much for you, and The Dragon Strikes isn't giving enough of a bonus in my opinion. Your Dragons already have Stealth or Deadly, and so you could use the space for other things instead.

It has potential, just needs some trimming down and fine tuning

Totally agree with NuFenix except "the dragon strikes". It grant you three additional power giving a dragon renown and can perform a critical strike giving a dragon deadly after defenders have been declared. However, stealth is useless.

... and other than making an example it can not be blocked with paper shield.

I'll answer a few of the questions with my reasoning, I'm curious to know whether my logic is sound or not (I still haven't had a chance to test the deck);

Mormont is the only character whose cost is 5, so I don't need to worry overly about the low amount of income modifiers in my deck (although there is the risk that I draw him and not Khal Drogo's Tent to obtain the extra income), but I have the extra copy to keep him alive until my opponent plays their reset plot card. As for the hatchlings being excessive, the games I have played with my original dragon deck, it can be difficult to draw duplicates, and the dragons are so key to the deck's strategy that keeping them alive is very important.

I do agree that the plot cards that benefit my opponent are risky, but I think the benefits outweigh the costs, as I already know exactly what cards will benefit my strategy the most and can pull them when they will be most beneficial. Counting Favours is simply to increase my draw, as draw is one area where Targaryen decks seem to suffer in my opinion.

Focused Offence can be used to win a match quite by surprise, especially if I have some Kingsroad Fiefdoms in play to ensure I go first. If I have multiple dragons (let's say 3) in play, and one of them is Rhaegal, I will get 3 power when they attack, plus the 3 I take for claim, plus any possible tokens I obtain with renown (Balerion has renown, The Dragon Strikes can be used to obtain renown, and Yunkai can be used to obtain renown). That's a lot of power in one round.

Using Qarth to add deadly after defenders are declared (same thing with the Dragon Strikes) will allow me to kill an opponent's stronger characters, as they are presumably using a strong one to block my dragons. It is less useful as I put more dragons in play, but when I only have 1 (or 2, in some cases), the value is much more apparent. It can also be used to allow me to defend with a dragon (especially if my opponent is using deadly, preventing me from defending with someone else who would die to it), as my agenda only prevents me from initiating Intrigue challenges, not from participating in them.

Citadel custom gives me an additional power challenge, which all my dragons can participate in if Daenerys is in play, so I can potentially receive 4 or 8 power tokens in a round, just through renown, in addition to the extra power token received through claim. Granted, it would be even nicer with a 2 claim plot card, I have chosen these plot cards to get the most vital cards out of my deck when I need them.

It's true that extra Dragon Lore could be used to play multiple dragons per round, but that would require multiple maesters in play, and any extra maesters I may have in play would probably be used to satisfy military claim. Also, it is not all that often that I actually have multiple dragons to play in a single marshalling phase (and if I were to play multiple dragons, I would probably choose to ambush one in).

Finally, Blood of the Dragon gives the bonus to the Dragon abilities that are used only once per phase (kill one character with X strength, destroy one location with X cost, and give each participating dragon 1 power), which will allow me to kill a seriously strong character and an expensive location under the right circumstances, and the additional power token is nice. For my remaining 2 challenges each round, it doesn't matter that the character will be knelt.

70 cards is somewhat fat, though it's only 10 over the minimum, but I won't know which cards to remove until I have had the chance to test my deck a couple of times. I'm leaning toward the Bitter Crones, as they have the potential to leave my dragons vulnerable to targeted kill, though I want to try them out to use Dragon Fear and Drogon's ability to take out annoying claim soak on my opponents' fields (such as Ser Davos and any cards with save attachments, lightbringer and Nymeria coming to mind), and I can just kill them to satisfy military claim, if necessary.

Forgot to mention the potential unnopposed bonuses in rounds where I use Citadel Custom or Focused Offence. I also forgot to address the point you made about having other characters to defend intrigue; I only have three cards in my entire deck that have intrigue, as I have opted for cards that are strong in military and power due to my agenda. Finally (really this time), I only have one Core set, or else I would have multiple Forever Burnings, though it may be the next thing to go from my deck, as this strategy really makes it's effect unnecessary, and only having 1 is not very helpful (though it's usefulness stems from the ability to pull it back from your dead pile every round).

Focused Offence can be used to win a match quite by surprise, especially if I have some Kingsroad Fiefdoms in play to ensure I go first. If I have multiple dragons (let's say 3) in play, and one of them is Rhaegal, I will get 3 power when they attack, plus the 3 I take for claim, plus any possible tokens I obtain with renown (Balerion has renown, The Dragon Strikes can be used to obtain renown, and Yunkai can be used to obtain renown). That's a lot of power in one round.

Mhm, a claim-2-plot would move one point less. But... you could do another power challenge. You could use a plot with a higher ini. You may be foreced to play this one as your seventh plot and this may really hurt you.

Finally, Blood of the Dragon gives the bonus to the Dragon abilities that are used only once per phase (kill one character with X strength, destroy one location with X cost, and give each participating dragon 1 power), which will allow me to kill a seriously strong character and an expensive location under the right circumstances, and the additional power token is nice. For my remaining 2 challenges each round, it doesn't matter that the character will be knelt.

Here: you spend three golds for a attachment, that can be discarded very easily. And in multiplayer you will mark the character with that attachment with "kill me first!". It's not that this card is bad, it's just to expensive to use with the dragons in my opinion.

70 cards is somewhat fat, though it's only 10 over the minimum, but I won't know which cards to remove until I have had the chance to test my deck a couple of times. I'm leaning toward the Bitter Crones, as they have the potential to leave my dragons vulnerable to targeted kill, though I want to try them out to use Dragon Fear and Drogon's ability to take out annoying claim soak on my opponents' fields (such as Ser Davos and any cards with save attachments, lightbringer and Nymeria coming to mind), and I can just kill them to satisfy military claim, if necessary.

Using 60 cards you can focus on your main characters. And every of this ten addional cards might be a non-dragon card. And without dragons you will not win the game. So it's about probabilities.

These are all good points, the main one that gives me pause for thought is the deck size, as I myself stated that Targaryens lack draw ability. I could easily take out a couple maesters, as I have more than enough to ensure that there is someone to wear Dragon Lore, especially if I'm using At the Gates. I could also scrap the Apprentice Collars for the same reason, though I like the idea of making Daenerys my maester, and they have 0 cost which makes them especially easy to get back with Lady Daenerys's Chambers. I'm strongly considering removing the Bitter Crones, as the strategy of this deck makes them somewhat pointless and they also create a risk for my otherwise safe (through duplicates) dragons. I suppose I could take out Blood of the Dragon, because it is quite expensive, and maybe remove Forever Burning too... What would you suggest for trimming the deck down a little?

Exactly in this moment. I'm working on a deck themed with bolton, shadow, winter and war. I've spend the last hour thinking about reducing the deck size to 60. I really don't like this task. I'm down to 67. Too much! ; )

I'd drop: 1x Balerion, 2x Advisor to the crown (hence there is no card using two influence), 1x True Queen's Harbinger, all Kingsroad Fiefdom (same reason as Advisor to the crown), Blood of the Dragon, 1 Maegi's Promise, 1 citadel custom, Forever Burning... (ten)

I guess you would like to ambush out your dragon's, but I'd probably use dragon lore to bring them out. Removing two maesters makes it difficult to you citadel custom. Removing the fiedoms will give you a worse initiate, but most plots have such a low ini, that you would not win ini in melee anyway. Put in another Dragon Lore and maybe you need another maester, for instance linked advisor. But then you have to remove other cards and the game begins again!

... one hour later it's done. 60 cards.