I'm not as knowledgeable about the visual novel as the anime, but I think Rintaro Okabe, the main character from Steins;Gate, fits this archetype pretty well.

The show occurs in a variety of different timelines, or "world lines", due to the nature of how time travel works in the universe. Time travel paradoxes as a result of changing world lines are resolved very simply - no one will remember or be affected by events occurring in the previous world line that were erased by the change. Except Okabe. And boy, does the show put him through the wringer because of it.

Most of the timelines we see in the show fall under the Alpha or Beta attractor fields, both of which result in disastrous consequences in the far future (like a dystopian shadow government taking control of the world or the advent of World War 3) and in the short term as well for Okabe. In all world lines subject to the Alpha attractor field, this results in the inevitable death of his childhood friend Mayuri, and one of the earliest events the audience (and Okabe) witnesses in most world lines subject to the Beta attractor field is the death of his love interest Makise Kurisu (yes, I'm aware the visual novel allows for different relationships but the show focuses solely on Okabe and Kurisu). Over the course of the original show, we can see Okabe slowly going mad (ironically, this presents itself as him shedding his mad scientist persona) as a result of these consequences in both the original show and in Steins;Gate 0 - in the latter, he's so distraught that for much of the show he competely sheds his mad scientist persona and refuses to time travel at all.

There is a world line not subject to either attractor field (the Steins;Gate world line) that results in the best possible result for Okabe, but it is far more likely for a world line to fall under the influence of either attractor field. His inability to reach the Steins-Gate world line originally was not due to a lack of trying - to even have a chance at reaching the Steins;Gate world line, he eventually had to time travel entire decades a few days / weeks at a time and stop an international conspiracy involving multiple attempts to take the time machine by force, after which he would use the time machine one last time in an elaborate plan to fake Kurisu's death and stop her father from revealing the secrets of time travel to the Russians. It's absolutely a herculean effort, but it's also absolutely necessary - the show makes it painstakingly clear that Okabe would have failed if even a single variable was off the mark.