By virtue about being a movie about Wolverine, it's already automatically awesome. Rule of Cool is most definitely in effect for this flick.
A successful Win Back the Crowd: After the much-maligned Origins (even Jackman was disappointed by it, feeling like it was too much of an undercooked X-Men 4 than a Wolverine movie), they adapted the long-requested and fan favorite Japanese arcs and dialed the scale back down to give full personal attention to Wolverine (while also treating Origins as near-Canon Discontinuity), and the result was a much-better-received movie that Fox immediately gave the greenlight for a follow-up.
The recently released Extended Train Fight clip.
Made of Iron Yashida Yakuza Enforcers going toe to toe with a potentially depowered Wolverine
One Made of Iron Yashida Yakuza Enforcer matches Wolverine whenever he has to jump over a traffic light, only being mildly irritated despite impacting into the top of a damn speeding bullet train.
Wolverine defying the laws of physics, by leaping and pretty much flying his ass over to the remaining Yashida Yakuza Enforcer still on the roof.
One flashback shows how Wolverine saved his benefactor: he saved his life at the atomic bombing of Nagasaki by throwing them both down a well and having his own body take the brunt of the blast.
After a hellacious fight with the Silver Samurai/ Yashida in which he has his adamantium claws cut off and almost has the life sucked out of him, Logan finally gets the upper hand in which he literally tears apart the giant mech with his bare hands before pulling Yashida close to him so that he can quip "Sayonara" then throws Yashida out of the building to his death.
Logan cutting open his chest to pull out the bug that Viper had implanted inside of him on his heart which leads up to an epic He's Back moment.
Her introduction in the bar. After predicting the future deaths of three men Wolverine had come to kill, she then shuts them all up with a few quick strokes of her katana. Her blade is in its sheath before we see just how sharp her strikes were.
Yukio also gets to show off her skills against Shingen in what may be one of the best swordfights in the entire movie.
The way Yukio takes out Viper.
Wolverine is ambushed by the Black Clan. They decide to fire arrows towards him, and he keeps going while pierced by arrows to the point Crucified Hero Shotdone with arrows. Badass doesn't even begin to describe it.
On the other hand, this is also the Black clan moment of awesome. If you think about it, those ninja probably do not have experience of dealing with Mutant, especially The Berserker with Healing Factor that would eat them like breakfast. Yet they subvert Conservation of Ninjutsu and did what Stryker in X2 could not do: capture Wolverine, alive, with minimal casualty.
Though it probably helps in that they had another mutant on their side who knows how to handle mutants. And is capable of generating poison so powerful that even Wolverine with his Healing Factor is knocked out.
Mariko taking two of Wolverine's sliced off adamantium claws and throwing them at her grandfather, impaling him in the skull and neck.
Wolverine finds a bear in the forest near a ruined camp site, dying of an illegal poisoned arrow. He seeks out the owner of said arrow, impales his hand to the bar with it, then repeatedly pours liquor on his hand while calling him out for antagonizing the bear and leading to the deaths of his friends. Had Yukio not stepped in, he probably would have killed every one of them.