I expanded the criteria beyond the title in the thread's OP. However, here are some examples:
Predator (1987): The alien tries each man's masculinity. Each man who dies does so in a manner befitting his swagger.
It's a well-worn idea that Predator is a film about masculinity. You have seven men each competing for alpha status, showboating their strength, stoicism, roughness and physical power. I'd like to go a step further. I'd like to suggest that the trials of the film are a test of masculinity, and that each man who dies does so in a way that mocks his masculine performance.
Let's go through the kills in order.
Scrawny, glasses-wearing radioman Hawkins is the first to die. Appropriately enough, he is the least successful in projecting his masculinity. He fails to crack bawdy jokes about his girlfriend's vagina, finds little useful intel for the team, and kills no-one during the guerrilla camp raid.
He dies when he runs after Anna and catches the attention of the predator. Out of context, the scene almost resembles a rape - Hawkins chases Anna and wrestles her to the ground. But this dynamic is reversed when the predator runs him through, drags him on his back, strips him naked and disembowels him.
Do you remember the joke he keeps telling? It's about how big his girlfriend's "pussy" is. The predator essentially carves him a fairly large one of his own. We see him moments later, dangling upside a tree, a gaping hole in his belly.
(A ghoulish detail: Judging by the naked marines Billy discovers at the start of the film, similarly skinned and upside down, the predator doesn't just disembowel men - it castrates them.)
Blain's not the weakest of the remaining crew, but he is certainly the showiest, with his enormous minigun. Blain has the most famous line outside of Arnie's: when he's shot in the arm, Ramirez rushes to his aid - "You're bleeding, man!". Blain's having none of it: "I ain't got time to bleed".
Indeed he doesn't. When the predator fires a plasma bolt through Blain's torso, the resulting wound is bloodless:
...Just like the others...no
powder burns, no shrapnel.
The wound all fused,
cauterized...what the hell
You remember Mac. He's the one who snatches Dillon from behind, threatening that if he blows the team's cover, Mac will "bleed him slow and quiet". He's probably the least mentally stable of the gang: by far the most menacingly violent, and with a propensity to talk to himself. When the Predator escapes the team's trap, Mac takes chase, babbling to himself, mentally decomposing into a violent trance.
You'd think that if anyone can out-sneak the predator, it's Mac, but the predator has him sussed fairly quickly. Sliding on his back, Mac suddenly sees a target on his wrist. It runs over his arm and head and - blam!
At first, it wasn't obvious to me how Mac might have prompted this death in particular. But I recalled two things: firstly, that Mac constantly, ritualistically shaves his head. He's doing it right from the first time we see him on the helicopter. So a headshot seems appropriate, though I'll admit the tie is a little weak.
(It may be the only one in the film, though, if you interpret Ramirez's death as neckshot.)
What's more, Mac's apparent madness makes his head his 'weapon'. He's just a little crazy, and that's supposed to make him scary, but there's no brain chemistry so unstable it can't be met with a well-placed microwave pulse. So mocks the predator.
Another matter I remembered is his threat to the predator the night before: "I'll carve my name into your skin". It's actually the predator that marks Mac, with his laser sight. The triangular target is the nearest thing we ever get to the alien's calling card, and it's traced over Mac's flesh slowly and carefully. Eventually it is visually 'imprinted' on his head by force.
A final, tenuous link: Mac promises to 'bleed' Dillon 'slowly'. Mac's own death seems to be the slowest: even when his forebrain is blasted apart, we see his body continue gasping and twitching until at least scene cut (and therefore implicitly longer). Everyone else dies fast.
Dutch's old friend from some unnamed army unit, Dillon is keen to show he hasn't softened with promotion into the higher ranks of military brass. He greets Dutch with an arm wrestle, and he loses. This turns out to matter.
Dillon has his arm lasered off and is shortly run through by the predator's claws.
This death is the most obviously telegraphed: it's the same arm. In the former scene, the arm is brought to the ground as it desperately pushes back; in the latter, the arm falls to the ground firing its weapon impotently.
Slim and wiry, Ramirez isn't a major presence in the movie, so this one's a little tougher to read. If you can't remember, he's the green beret who gets hit by the log trap, sent flying and landing in a crippled heap. He limps along for a little while before being unceremoniously shot in the neck.
Ramirez's greatest swaggers happen in the guerrilla camp raid. Carrying a six-shooter grenade-launcher, his well-placed blasts fling enemies through the air over and over. I counted four shots of men being thrown towards the camera by explosions in that scene, and three of them belong to Ramirez. (The other is a grenade from Billy). The film fixates on these shots enough to conclude they're supposed to be impressive, so it's a pointed irony that Ramirez is thrown through the air in a similar manner.
Not convinced? There's a little ad-hoc addition to the original screenplay. When Blain boldly asserts he "ain't got time to bleed", Ramirez quips back: "Oh yeah? Have you got time to duck?". Ramirez is later crippled by a fast-moving log to the chest that everyone else jumps under.
Billy doesn't swagger. He acknowledges his fear, listens to his superstitious instincts and generally prefers to act rather than talk. He is granted the most noble death of all the soldiers: an off-screen fate that preserves his mystery and lets us imagine - or rather hope - he died bravely.
But he dies all the same, because he chooses not to run. And that is the difference between him and Dutch. Running is how Schwarzenegger's character survives. He runs and falls into the river, covering himself in mud. He backs into a corner, camouflaged thermally. He lets the predator chase him into a trap, which eventually proves the alien's undoing.
Of course, there's a practical reason for Dutch to retreat: the way power shifts between man and monster makes the scene engaging and tense. It modulates our fear and hope. But it's curious how feminine our hero's cries are when we hear them from the Predator's POV; they're high pitched and whimpering. Dutch doesn't hide his pain or his fear; in fact he's actually the least ostentatiously masculine of all the squadron - his masculinity comes from acting with instinct and knowing the land, not swaggering performance.
Turns out, that's the only real masculinity that actually matters.