Among the Akatsuki's members in Naruto Shippuden are Hidan and Kakuzu, often referred to as the immortal duo. This is a bit of an exaggeration. Kakuzu is extremely difficult to kill not because he's truly immortal but because he can have up to five hearts at any time, and can only be killed after all of them are destroyed. He could replace them by taking hearts from those he killed, gaining access to their Chakra Natures in the process.
While this makes him a frightening opponent, he was eventually killed in battle by Naruto and Kakashi. Hidan, on the other hand, is perhaps the only truly immortal character in the series, unless you count Orochimaru's ability to maintain his consciousness through curse marks.
How Hidan's Immortality Works
The source of Hidan's immortality lies in his fervent worship of the evil god Jashin. Little is known about the religion, to the extent that the Leaf Village once thought Hidan had invented it. Hidan believes that Jashin requires regular sacrifices, and thus is a prolific killer. His immortality is implied to be the result of sacrificing many people at once to Jashin, but the exact mechanism for how he acquired it remains mysterious. Ryuki, another Jashin follower introduced in Boruto, is not immortal, and the plot centers around him trying to gain immortality by sacrificing a large number of young women. This implies that not all followers of Jashin are immortal, and indeed Hidan is the only confirmed case.
The extent of Hidan's immortality is frightening. He has survived multiple stabbings, a massive blast of fire from the Two Tails, decapitation, and having his body blown to pieces by paper bombs. If stabbed or burned, he can regenerate from his injuries rapidly, although not as fast as Orochimaru. The only way Hidan can truly die is from malnutrition. Aside from that, Hidan can't control his body if decapitated until his head is reattached, and he retains the ability to feel pain. The latter, however, is something he derives immense pleasure from.
How Strong is Hidan?
In battle, Hidan fights using a triple-bladed scythe, which can also be used as a long range weapon because it's attached to a very long cable. Hidan is also extremely fast and agile, making it difficult for enemies to fight him at close range. Hidan's main objective in battle, however, is not to kill opponents with his scythe but merely to draw blood with it. After tasting his opponent's blood, the real nightmare begins.
Hidan's main technique is his Curse Jutsu: Death Possession Blood. After tasting his opponent's blood and drawing a symbol of Jashin in the ground with his own, Hidan's skin turns black with white skeletal markings, and he becomes a living voodoo doll. As long as he stays inside the circle he drew, any and all injuries inflicted on Hidan are also inflicted on his opponent. Because Hidan can't die, he can easily kill opponents using this technique without harming himself. Hidan used the technique to murder Asuma Sarutobi, a powerful Leaf Village Jonin, with relative ease, finishing him off by stabbing himself in the heart.
Shikamaru, wanting revenge for Asuma's murder, fought Hidan while Kakuzu faced his teammates and Kakashi. He managed to outsmart Hidan by substituting his own blood with Kakuzu's, costing the latter one of his hearts. After binding him with his jutsu and suspending him ove a pit surrounded him with paper bombs, Shikamaru managed to blow Hidan's body to pieces, after which he buried him alive. It's implied that for the remainder of Naruto Shippuden, Hidan was alive but slowly starving to death at the bottom of the pit.
Although immortality is a recurring theme in Naruto, Hidan is still the character that came closest to actually possessing it, making him one of the series' strangest and most powerful fighters. And had he been less reckless and a bit more intelligent, he may have been nearly unstoppable.