Dick Grayson has almost reached Batman to a point and is believed literally and figuratively to be his successor.
Master Detective: Grayson is a world class detective, second only to the likes of Batman. He was rigorously trained by the Dark Knight in everything from escapology to criminology, fencing, stealth, disguise, and numerous other combat/non-combat disciplines.
Grayson is a prodigious natural athlete, possessing a peak human level of agility/acrobatic skills. He is regarded as the greatest human acrobat in the DC universe. Batman himself is an incredible athlete in agility, and is at peak human perfection, but even he gives the advantage in that area over to Nightwing. He is the only person on Earth who can do the quadruple somersault.
He has been taught by Batman, the ability to instill fear into others. While not as efficient as Batman in this category, he still uses this ability effectively. A prominent example of his interrogation technique was his tactic of threatening to allow Gorilla Grodd's soldiers to drown unless he divulged who had sent him to attack New York City (A threat he obviously was not going to follow through with).
Master Martial Artist
As Nightwing, Grayson is a master of dozens of martial arts disciplines, with an emphasis on Aikido and Escrima, taught to him by Batman. His preferred fighting style combines Escrima, Judo, Savate, Capoeira, Aikido, Boxing, Wing Chun, Hapkido, Jeet Kune Do, Taijiquan, Ninjutsu, and Bojutsu with his acrobatic abilities. He is considered one of the finest human combatants in unarmed combat, almost on par with Batman. He has fought and held his own or defeated some of the best fighters in the world. Prominent examples include Ra's Al Ghul, Deathstroke, Jason Todd, Shrike, Red Arrow/Arsenal (Roy Harper), Azrael, and even Batman himself.
Through his martial arts training with Batman, he has become an expert on almost all types of weaponry.
Master of Stealth
His training has made him a master at stealth capable of easily breaching high security facilities without being detected. He has been compared to Batman, in terms of stealth and has been stated to be as good as Batman in this field. He has even snuck up on Batman himself.
As a result of his training in ninjutsu and with Batman, Nightwing almost never misses his targets, 9/10 times he's successful. He has been practicing accuracy since the early days of his training as Robin and is on par with Batman in terms of accuracy.
Nightwing has been trained in hunting and tracking techniques by Batman. He is a master tracker, comparable to the Batman.
Master of Disguise
He is proficient in the art of disguise as having been taught by the Batman himself.
Batman has trained Nightwing in this ability since his earliest days, in turn making Nightwing, a master escape artist. Though not as good as Batman, he is proficient enough, to be only second to the Batman in this category.
Peak Human Conditioning
Dick Grayson possesses the peak athletic strength and endurance of a man who regularly engages in intensive physical exercise. His physical attributes exceed that of any Olympic level athlete that has ever competed. His strength, speed, stamina, reflexes, agility and coordination are at peak human perfection.
Peak Human Strength
He is one of the strongest non-metas on Earth. Although he relies on his speed more than his strength, he has shown remarkable strength throughout his career, though not as great as Batman's. He has dented and nearly ripped through steel with a single kick, defeated KGBeast physically, managed to knock down Blockbuster with a blow, punched the meta-human Barry Pierce through a concrete wall, and supported nearly 1000 lbs. of rubble when attempting to save people from a burning building.
Peak Human Reflexes
Nightwing's possesses reflexes that have enabled him to dodge point blank gunfire from multiple opponents at the same time.
Peak Human Speed
He has run at speeds greater than the finest competing athletes. He has been stated to be even faster than Batman.
Peak Human Endurance
Nightwing's endurance is greater than an Olympic Decathlete. He can exert himself at peak capacity for nearly an hour without rest before showing any signs of fatigue. His lung capacity is so great that he is capable of holding his breath underwater for 4 mins.
Peak Human Agility
He has honed his agility to top human physical perfection. He is as agile as one could be without being considered superhuman and has even been told that he has shown agility that should be beyond human capabilities. He is considered to be the most agile human being in the DC Universe.
Peak Human Durability
He has been thrown through entire walls, by Roland Desmond, and immediately rose back up to finish the fight, survived an entire building collapsing, has fallen of the top of a building when his and has sustained other extreme forms of punishment, and has survived it all without any serious injury.
Having had the finest education as Bruce Wayne's ward, he speaks with fluency in English, French, Chinese, Spanish, Russian, Japanese, German, Swahili, Mandarin, Cantonese, and is possibly fluent in other languages. He has some knowledge of Romany and the alien language of Tamaran.
He is also a brilliant and experienced strategist with superlative leadership skills, having served as leader to the Titans, the Outsiders, and even the Justice League. Additionally, Dick's efforts to remain in contact with other heroes makes him a master at rallying, unifying, and inspiring the superhero community, a skill in which he has surpassed his mentor.
Like his mentor, Grayson is a brillant, albeit looser tactican who relies more on intuiton and timing, rather than meticulous preparation.