Hoard of the Dragon Queen [IC. 2014 rules]

Dragon str save 26

While Draylin arms the ballista, Thistlewick and Montar both manage to land an attack on the fast-approaching dragon. For such a huge creature, the necrotic cantrip of the druid feels like the bite of a flea. Montar’s crossbow bolt feels like a toothpick between its scales, but at least it strikes deep enough. For a second, the blaze from the dwarf's fire rune envelops the dragon, but the beast moves in a spiral and shrugs off the chains with a mind-blowing fluidity, easily avoiding getting restrained.

Governor Nighthill and Escobert have moved toward another of the ballistas and spend their turns arming and aiming it.

The defenders of the third group have positioned themselves on the northernmost parapet. They too unleash a volley of arrows toward the beast.

Attack: 20 Damage: 5
Attack: 18 Damage: 9
Attack: 9 Damage: 10
Attack: 16 Damage: 7
Attack: 7 Damage: 9
Attack: 15 Damage: 6
Attack: 9 Damage: 6
Attack: 13 Damage: Unable to parse dice roll.
Attack: 8 Damage: 6
Attack: 6 Damage: 6

Over to Tam. Aiming the ballista and shooting it each require an action. 

[Can Tam use both of her actions, one to Aim and one to Fire? It seems like the Utilize action would still allow me the attack action. And the way you described it, one to load and one to aim and fire seems to support this. If this is wrong, let me know.]

Tam takes a deep breath and assesses the dragon, using her keen observational skills to line up a perfect shot. [using bonus action to activate Insightful Fighting. 12 Insight check versus the dragon's Deception to allow me to use Sneak Attack]

Aiming carefully, she unleashes a shot, not sure if it is good enough to hit [8 roll + 1 dex + 6 = 15 to hit the dragon with the Ballista. If I get proficiency bonus to that it is 17, but I doubt I do. In case that actually hits 22 damage + 9 for sneak attack in case that went through].

Because Draylin helped with loading it, the ballista actually doesn't need much aiming, so will allow both aim and fire as an action together. 

Dragon deception 16

Tam pulls the heavy trigger, and the giant bolt is released with a powerful snap. For a brief second, it looks like it might pierce one of the dragon's wings. However, sensing the danger, the creature folds its wings tight against its body to let the bolt whistle harmlessly by, before spreading them wide once again.

It hovers about fifty feet away from the parapets, and you all watch in horror as a bright, crackling light begins forming deep inside its chest. That electrical energy rises like a surge of lightning up its long neck and gathers into a violent ball between its jaws. It grows larger and larger until it erupts in a blinding line of lightning directly toward the defenders on the northernmost side (Group 3).

They each desperately try to jump aside to avoid the eviscerating breath weapon:
Dex saving rolls:
6
7
2
7
9
20
7
20
8
8

For those, who don't succeed, the lighting deals 53 damage. 

Recharge: 6

Only two of the defenders manage to jump away in time to avoid getting completely obliterated by the torrent of lightning energy, although they suffer severe burns. Even more worrying, the crackling light begins forming deep inside the dragon's chest again!

Leosin and another guard scramble over to the final unmanned ballista, working frantically to arm and prepare it.

Groups 1 and 2 unleash another volley of arrows, although they visibly struggle to aim their bows, too traumatized after the complete destruction they just witnessed:

Dice rolls because the dice roller is broken yet again:

Attack: 17 Damage: 6
Attack: 6 Damage: 7
Attack: 7 Damage: 3
Attack: 8 Damage: 3
Attack: 19 Damage: 5

Attack: 6 Damage: 9
Attack: 17 Damage: 7
Attack: 8 Damage: 9
Attack: 13 Damage: 9
Attack: 7 Damage: 7

Attack: 10 Damage: 5
Attack: 6 Damage: 5
Attack: 13 Damage: 7
Attack: 6 Damage: 7
Attack: 5 Damage: 6

Attack: 17 Damage: 8
Attack: 15 Damage: 5
Attack: 7 Damage: 4
Attack: 23 Damage: 5
Attack: 14 Damage: 7

Round 2

The air is thick with the scent of ozone, scorched flesh and burning stone. The blue dragon hovers 50 feet out, its throat pulsing with a brilliant, gathering electrical storm. Group 4 frantically attempts another round of attacks, although the hands of many tremble so hard they can barely pull their bows taut.

Attack: 15 Damage: 6
Attack: 7 Damage: 6
Attack: 10 Damage: 6
Attack: 18 Damage: 9
Attack: 13 Damage: 10

Attack: 5 Damage: 3
Attack: 19 Damage: 9
Attack: 16 Damage: 4
Attack: 20 Damage: 6
Attack: 14 Damage: 8

Thistlewick, Montar, and Draylin, you are up!