I Must defeat him = Only I am allowed to Defeat him.

Even if it means my life = Heroic Sacrifice

Plus the Picture in Question is a Visual Spoiler from an obscure manga compared to the well know James Cameron Movie, and there for people can more easy associate with it.

It is a fact that the Movie is known to more people, but also my point is that the terminators are very good exemple of determinators if you think about it.

In the first movie Arnie is an unstoppable force 'determined' to get his goal, even getting to the level of walking squeleton all in order to execute his mission. Of course he his but a machine and probably not affected by our petty humane emotions but...

In the second movie; the protagonist, while being a machine, the audience would think not at all affected by whether or not he lives or die, succeed or fails, etc. in fact just keeps goin on, after his apparent on-screen death, until he succeed in getting the big bad, saving his friends and finaly sacrificing himself for the greater good (if you discard the other movies of course)

At least from what I've read from the page about images just waking up I'll get a link later Images should be as well known as possible without Spoiling key pieces of the plot unless it is a spoiler trope.

Just A Face And A Caption ?

No idea what that image was supposed to be. Let's just skip the picture, if it is going to be this much trouble.