First things first, 'Based on a true story' is not a genre.

"Mike and Dave Need Wedding Dates" is based on a true story, but I don't think you want examples from a romcom.

But you're right, inspirational action dramas based on true stories do have tropes.

Captain Phillips, Deepwater. Sully.

The cliched arc of a protagonist in this type of story might be...

1. A hero (nearly always male) with a flaw (alcohol, works too much, perfectionist) has something to lose (a family).
2. He steps up to protect a group of people (co-workers, passengers, survivors).
3. He uses his specific skill (pilot, boat captain, oil rig tech, cop) to defeat a singular obstacle (a leaking oil rig, terrorists, hijackers) while battling the institutions of unseen corporate forces (oil company CEOS, Transportation Safety Board) and he has to do all this while racing against the clock.

There are also cliches of tone.

In these inspirational BOATS, as you call them, the tone comes from grounding the story in reality. These are real people, so these movies throw in mundane details that movie-goers recognize as real life, ie true story.

So if in most inspirational BOATS action dramas, an ordinary joe answers the call with extraordinary courage...

Tone cliches of an ordinary joe might include: He has a family, a blue collar job, a drinking problem, a dog or motorcycle he loves, friends he jokes with, a favorite kind of sandwich, an internal wound (death of a loved one, divorce) that he refuses to face.

Tone cliches of extraordinary courage: an ordinary joe with no business facing a cataclysmic event chooses to face it anyway.

As far as theme goes, movies are about morality and doing what's right, or at the very least presenting right and wrong, and increasingly nowadays, blurring the lines between those in order to help us decide for ourselves the difference.

So on the inside, if he's running from commitment to a girlfriend who wants to get married, you want to drop a bomb on him, make him face life/death, make him decide what's meaningful in his life, make him choose his purpose; and if it's a happy ending movie, he both saves the world AND commits to the girlfriend, having faced his own demons/mortality.

By the way, in real life, Captain Phillips crew say he was no hero and in fact was a dirtbag.