Even as your executioner looms over you, the grief over losing your parents--and Baral's stifling countermagic--prevents you from fighting back. But one last spark of defiance still burns inside you, and it's begging to be freed.
Captain Baral has a monoblue control deck with countermagic, card draw, evasive creatures, and some ways to keep opposing creatures tapped down.
Most of Baral's countermagic doesn't actually get rid of the threat: Remand returns it to your hand, and Memory Lapse returns it to the top of your deck. The former isn't much of a problem at all since it's pure tempo and Baral's deck generally isn't aggressive enough to take advantage of that. He does have two Arcane Denials, however, which do hard counter a spell, though it gives Chandra +1 card advantage in the process. You shouldn't worry much about the countermagic and just play your cards, though; Baral still gets the same tempo value if you don't play a card as if you do, but if you do and he counters it, he has one fewer piece of countermagic to use later on. The exception is in the late game if you're trying to resolve something important; in that case, you might want to bait out possible counters with cheaper irrelevant cards, which Baral typically falls for.
Baral has only five real threats in his deck: two Gold-Forged Sentinels and a Goliath Sphinx; the two Dungeon Geists can also be an issue, but they can be easily burned out with most of Chandra's burn spells. Save your Manic Vandals for the Gold-Forged Sentinels. Goliath Sphinx is the hardest to deal with, so try to be prepared to burn its 7 toughness out if Baral taps out for it; he'll probably also block with it, so sending some creatures in might help to get the extra damage you need to finish it off with burn (make sure to think about his possible blocks and be sure you're satisfied with the possible results, though). If you can deal with those threats, though, his deck does nearly nothing.
As far as Chandra, her deck's upgrade is well-suited to this matchup. Exquisite Firecraft's spell mastery effect is actually relevant against Baral's deck, so it can be useful to push the final 4 damage to Baral without him being able to stop you. And Flameblast Dragon will probably win the game, or very nearly do so, if you're able to attack with it even once, due to its triggered ability.