TRAINING
Went through 6 months of intense training from Batman before he became Robin (Robin Annual #4)
In his Post-Flashpoint origin he was trained for untold months by Batman in the martial arts among other areas (Nightwing v2 #0)
Bruce is shown putting a young Dick Grayson through numerous intense training programs before he became Robin (Secret Origins #1)
Nightwing #25:
While blindfolded he shown training Robin/Tim Drake (Red Robin) in balance, reaction time, & agility by taking him on a trip on top of a train. He mentions how Batman took him through the same training exercise when he was Robin.
Later on, a gang attempts to ambush the duo but are easily beaten up
Dick also showcases how acute his senses are by knowing where he is at all times being in tune with his environment and saving Tim from falling. We then see them jumping onto another train with Dick doing it with ease
Received additional training when he was older from the legendary martial arts master Richard Dragon (Richard Dragon #7)
KNOWLEDGE
Is a master of a half dozen martial arts styles with an emphasis on Aikido (underlined in yellow) (Nightwing Secret Files & Origins #1)
Officially mentioned as being only 2nd to Batman in fighting skill (DC Comics Encyclopedia vol 2)
As a rookie Robin, he impresses Shrike (League of Assassins member and martial arts master) with his display of vast skill in a handful of martial arts styles and very briefly becomes one of his students (Robin Year One #3)
Training Robin/Damian Wayne (son of Batman/Bruce Wayne who already has League of Assassins training) in martial arts (Batman #688)
Trains Nightrunner in martial arts among other things for weeks to become the Batman of France for Batman Inc (Batman Annual #28)
Thunder reveals that she's received training from Nightwing and uses that training along with her meta human super power to defeat the much more powerful Grayven after Martian Manhunter is taken down by him (Outsiders Five of a Kind: Thunder & Martian Manhunter)
Blocks a death touch technique that Batman once showed him (Nightwing Mini #4)
Using several nerve strikes against black ops trained & enhanced super soldier Lyle Blanco that would've taken out anyone else. However, they don't work here only because of Blanco's super human durability and seemingly being impervious to pain (Batman #690)
Able to quickly put Garth aka Aqualad into a martial arts grappling submission hold although it doesn't work only due to Garth's super strength (Titans Hunt #1)
BATTLES
Easily defeats the super spy Nemesis (Thomas Tresser) while attempting to reason with him (Nemesis The Impostors #2)
Vs Goode Ole Bernie
Highly skilled assassin that mastered the death touch technique (Nightwing Mini #1)
Ambushed by Bernie in his apartment, he still gets the upperhand on the assassin (who's using a knife) and chases him off despite being in his civilian clothes which holds back his full combat skill as he notices in the fight when something is off about him and mentions it later on (Nightwing Mini #2)
Defeats Bernie in the rematch (Nightwing Mini #4)
Displaying excellent combat skill, speed, and agility to defeat Matatoa who's an undefeated warrior who feasts on people's souls to remain immortal plus takes on their best qualities/skills and wanted Batman's soul for this purpose (Gotham Knights #17)
vs Vigilante (Dorian Chase)
After being ambushed by the super human 21 Tigers soldiers, he fights Vigilante again and decisively defeats him (Nightwing #136)
Dominates Vigilante in another battle plus shows off his reflex speed as he hits Vigilante with a batarang before Vigilante could shoot him. Also, Vigilante mentions Batman's (Dick's) strength and admits he can't win in hand to hand combat (Vigilante v3 #10)
Vs Shrike (protege of the original Shrike and League of Assassins member)
A very weakened Nightwing saves Canary and defeats Shrike (Nightwing #58)
Defeats Shrike yet again more decisively while angry and leaves him as a message to Blockbuster (Nightwing #91)
Defeats Arsenal (Roy Harper the protege of Green Arrow) one of the best marksmen in the DCU who can use anything as a weapon with Checkmate special ops training (Justice League: The Rise of Arsenal #3)
Decisively defeats Jason Todd (aka Red Hood and the second Robin) despite being electrocuted, gassed by Scarecrow's fear toxin, and taking bat tranquilizers to the face winning over Batman's cowl (Battle for the Cowl #3)
Gets the upperhand on martial arts master HWA Rang who's physically the strongest member of Lady Shiva's Circle of Six and deceptively very fast for his size (Richard Dragon #3)
Defeats Deathwing who's an evil version of himself from an alternate reality (The New Titans #100)
Stalemates Azrael (Michael Lane the former 3rd evil Batman) in a sword fight (Azrael Death's Dark Knight #3)
Bested Ra's Al Ghul (who has stalemated Batman several times in prolonged battles) in a sword/melee fight (Nightwing #152)
Grayson #18:
Vs New 52 Bronze Tiger
- Dominating Bronze Tiger in hand to hand combat
- Then once again while fighting other opponents
Defeats The Orphan aka David Cain (father of Cassandra Cain) in melee combat which takes place mostly off panel (Batman & Robin Eternal #14)
Stalemates Batgirl (Cassandra Cain) who's one of the top ranked martial artists in the world until the fight is broken up by Alfred (Batman and the Outsiders v2 #8)
Able to fight evenly with Batman his famous mentor & teacher in a bloody and brutal battle inside the batcave that's left in a complete wreckage thanks to their prolonged battle. He also passes Batman's test who wanted to make sure his will wasn't broken and declares himself the winner at the end once Batman decides to stop the fight (Nightwing v2 #30)