The user can overcome their limitations/weaknesses, whether personal, from their species or inherent to their other powers, becoming either more resistant or completely immune to said weaknesses. This can be accomplished through ascendancy into a more divine-like state or natural evolution like performing repeated non-lethal exposure to said weakness; for example, a vampire may become immune to sunlight or a werewolf resistant to silver.
Red Stone of Aja (JoJo's Bizarre Adventure Part II: Battle Tendency)
Lapis lazuli (The Vampire Diaries)
Saya Otonashi (Blood+) has been able to control her blood-thirst through regular blood transfusions and eating large quantities of human food.
Son Goku (Dragon Ball) overcame his weakness to his tail being squeezed through extensive training.
When he still had a tail, Vegeta (Dragon Ball Z) was able to overcome the Saiyans' traditional weakness of having their tail squeezed.
Nappa (Dragon Ball) has overcome the Saiyans' weakness of having their tail squeezed, as Piccolo discovers the hard way.
Alucard (Hellsing) is immune to all vampire weaknesses except the most holy of Christian artifacts, such as Helena's Nail.
After entering Gear Fourth - Boundman, Monkey D. Luffy (One Piece) is able to retain his natural rubber state despite being coated completely with his Haki which should normally neutralize it, allowing attacks that would normally harm him to simply bounce off.
Saitama (One-Punch Man) broke through his human limitations after 3 years of training.
Due to its unique composition, the Crystal Onix (Pokémon) is immune to water and Water-type attacks, unlike other Onix.
The Frog Hermit (Ranma 1/2) has transcended the limits of his jusenkyo curse, allowing him to talk and fight as if he was still in his human form.
As he was originally human and turned into a vampire, Tsukune Aono (Rosario + Vampire) is unaffected by the traditional vampire vulnerability to water.
In spite of him becoming a vampire, DIO (JoJo's Bizarre Adventure) is immune to almost any weakness such as cross, he's only vulnerable to sunlight and Ripple/Hamon users.
Despite his former title as the world's weakest hunter, Sung Jin-Woo (Solo Leveling) was able break through the limitations of an average hunter after becoming a Player and the constant battles and training workouts within the System's quests.
Through centuries of dedicated training, Crom Cruach (Highschool DxD) became a transcendent dragon, completely surpass his natural limitations.
After being implanted with the Mantra Reactor, Asura (Asura's Wrath) is able to freely channel his Wrath Mantra without fear of it backfiring and destroying his body.
As a dhampir, Rayne (BloodRayne) is immune to holy items and resistant to sunlight and water.
Kain (Legacy of Kain) has developed immunity to sunlight and certain forms of water (rain, snow, etc.)
Alex Mercer (Prototype) developed an immunity to the anti-Blacklight poison Bloodtox with repeated exposure.
The enhanced Type 2 Las Plagas (Resident Evil) were able to tolerate direct sunlight, though flash grenades were still fatal to them.
Rahab (Legacy of Kain: Soul Reaver) was able to overcome the vampire race's traditional vulnerability to water.
By consuming Rahab's soul, Raziel (Legacy of Kain) was able to overcome his vulnerability to water.
Daurgothoth, the creeping doom (Forgotten Realms) has transcended not only the limits of his undead body, but also the limits of the dragons species as a whole, developing new breath attacks that he shouldn't be able to use, as well as developing other abilities that should be impossible for him because of his undead status.
Dark Sister (Valkyrie Crusade) is a Vampire that is immune to all of an vampire's weaknesses, such as sunlight and holy powers and objects.