Character advancement in 7th Sea is based entirely on completing stories. This includes your Hero Story itself and the Gamemaster Stories created for the group as a whole to follow. The difference is that the reward of a Gamemaster's Story isn't set when it is created. Instead, once a band has completed a story they get to choose one of the advancements available to a Hero Story.
Languages: All (Linguist)
Virtue - The Sun - Glorious - Activate when your character is the center of attention. For the next Risk, when you determine Raises, every die is a Raise.
Hubris - The Lovers - Envious - Receive a Hero Point when your Hero becomes enamored of someone they shouldn't.
Got it! - Spend a Hero Point to immediately pick a lock, crack a safe, or disarm a trap. (2 pt - Hunter)
Sniper - You get a bonus die when you make an Aim Risk with a long-barreled musket, longbow, or crossbow. (3 pt - Hunter)
Sorcery: 2 - Dar Matushki - 4 Gifts, 2 Restrictions (2 pt per level - Touched by Matushka)
Survivalist - If you are in the wilderness you can forage to find enough food for yourself and five other people. In extreme circumstances, you can find enough for yourself and two other people. (1 pt - Touched by Matushka)
Poison Immunity - Poison never affects you aside from some minor potential discomfort. If the poison would ordinarily kill you, it might only make you vomit instead. There are no other effects (2 pt - Bonus Advantages)
Linguist - You speak all Thean languages, even the Dead ones. (1 pt - Bonus Advantages)
Eagle Eyes - As long as you have a clear line of sight, you can see perfectly out to a distance of one mile. If you use a spyglass you can pick out fine details, such as the inscription carved into a wedding band. If you make a Risk that relies heavily on your keen vision, you gain 1 Bonus Die. (2 pt - Bonus Advantages)
Hunter - Earn a Hero Point when you use your hunter's acumen to save someone from danger.
Touched by Matushka - Earn a Hero Point when you teach someone a lesson in a way that would make Matushka proud.
Ending - Earn the love of the baron's daughter
Reward - This is 5 Step story resulting in Panache +1.
Step One - Charm the baron's daughter at the celebration.
Step Two - Gain the lady's favor.
Step Three - Be kissed by the lady.
Sorcery: Dar Matushki
Serpent Hair - Spend a Hero Point to tranform your hair into serpents. The extra eyes and other senses give you a Free Raise on Notice Risks for the rest of the scene. (My Creation)
Petrifying Gaze - Spend a Hero Point to reduce an opponent's Raises that round by your Intimidate rank due to being temporarily paralyzed. (My Creation)
Curative Blood - Spend a Hero Point to transform your blood into an antidote for any poison. You suffer a Wound for each person you want to cure. If the poison is supernatural in nature, you suffer a Dramatic Wound. (My Creation)
Command Snakes - Spend a Hero Point to call and issue a command to a snake. If there are no snakes in range or the animal is unable to obey the command, the GM refunds your Hero Point. If the command requires a Risk the animal rolls 5 dice but you decide how it spends the Raises. If the task is particularly appropriate to the snake you called, then it gets 2 bonus dice.
Modesty (My Creation)
Limit: You must not act with the motive of proving your superiority.
Penance: You must help someone downtrodden recognize their own worth.
Endurance (My Creation)
Limit: You must not complain about misfortune or ill treatment.
Penance: You must seek someone facing unjust suffering and help them through it.
I tend to feel that I did not build in enough 1 pt or 2 pt stories into these as it made it difficult to get that 1st point of Convince or other such abilities. I did take lower-value advancements for several story rewards however. The story system really works to give a carrot for the players to follow. If they want to make any advancement, they have to chase story leads. That said, they can still end up doing their own thing and completing a minor side mission or else something that pops up into their line of sight. It just means that they might slowed down at completing the current ongoing major plot line.
I'm not entirely certain you're meant to include Episode and Character Stories as part of the lead up to the steps for the Season Story, but it makes logical sense to do so. I will note that the amount of which I felt it necessary to imagine into being for the theoretical is another nod to how narrative driven this game and its advancement are. The mechanics lean quite heavily toward the Stat-driven sort of gaming, but the overall feel of the game is extremely narrative and especially cinematic in nature. There's a lot of feel that is reminiscent of Fate or, closer, Hero System in terms of how the player is able to drive parts of the story along.
Advancement in this game is a good mix of lateral and vertical. It also seems to tolerate a fair mix of character advancement levels as there is a set cap of Skills and Traits at 5. For that matter, you are not allowed to have more than 15 total points of Traits, so if I had pressed toward the gorgon getting her romance with the Baron's Daughter and that improvement to Panache 4, that would have been the last improvement I could take in Traits. However, it would be possible to shift Traits around still.
The story system also makes it really easy to tell when characters have received some focus and gotten a chance to shine or not. You just have to look at their personal story and see what they are looking to do and whether or not that has changed recently. For that matter, this story system seems to be something that could be done to track character's story moments in other systems as well.
Depending on the GM, this system could have a very speedy advancement curve or else an extremely slow one. However, even with a fast advancement curve you are unlikely to have the problem of "out-leveling" any content or enemies, meaning you can keep to the same sort of threats throughout the game rather than constantly having to upgrade to new enemies. Even so, you will start moving in scope as you can tell from the simulation I ran here.