Season 1:

Pulls a man with his Grapple Gun so hard he sends him flying onto a Car and damaging the window.

Crushes the side of a man's head off of a Brick Wall.

Snaps / Breaks a man's arm.

Throws a Trash Can.

Crushes a man's head off of broken Glass.

Tosses a man out of his car.

Throws a guy through a wooden pallet.

Crushed Batman's neck with his foot, Batman is also wearing his suit which likely gives additional protection.

Robin was able to resist the strength of Nuclear Dad, who could rip off car doors with ease.

Season 2:

Lifts Jason to the roof with one arm.

Season 1:

Makes a man splatter blood on a wall with his punches.

Hits a thug with a gun so hard that he makes him bleed and his blood splatters on a wall.

Snaps a man's leg with a kick.

Knocking around the Superhuman Nuclear Family with his strikes.

Season 2:

Ragdolls Jason with a kick.

Season 1:

No-Sells jumping off of a Building and landing on a Car without his Cape (SUPERHERO LANDING).

Takes multiple hits from the Nuclear Family.

Gets rammed through a window and onto a car, and is fine, as we can see around 1 minute and 10 seconds later he has already managed to put his Outfit on and equip his gear.

Isn't really bothered as he digs a tracer out of his arm with a scalpel.

Is barely affected by a Taser Rod (Note he has also been drugged here).

Season 2:

Took 6 hits, a flashbang, and 2 stabs and was fine to carry on fighting, was only ultimately put down by Slade's 10 hit combo.

Takes more hits from Deathstroke + Electric Baton Strike.

Season 1:

Aim dodges a gunshot.

Dodges a bullet.

Catches a Shuriken.

Season 2:

Dodges a blast from Dr Light.

Dodges a throwing knife.

Season 1:

Leaps across rooftops at an incredible speed.

Flips and maneuvers around Sword Strikes.

Scales down Wayne Manor using a tree before he was Robin, due to his Acrobatic Background.

Has a Grapple Gun that he can throw objects / people with.

Has Smoke Bombs which he can Use to Disappear.

Has Robin Shurikens which he is very accurate at using, we see this when he throws them at the thugs hands.

Has a Baton which can Expand in to a Staff and Retract back into a Baton.

Cape can tank Dr Light Blasts (Same blasts can flip cars).

Nightwing Suit:

It's a Nomex triple-weave Kevlar shell, electrically insulated and light-sensitive. It has fewer body inlays than the old one, which will allow you to utilize your circus skills. "Move more, get hit less." That was our mantra.

The mask has a built in Wireless Transmitter and Starlight night-vision lenses.

Season 1:

Shows exceptional Combat Speed with his Baton / Staff, stomping 2 guys in 4 Seconds.

Stomps 10 Guys in 57 Seconds without being tagged.

Single-handedly, Stomps 3 Members of the Nuclear Family. Note: The Nuclear Family casually beat Hawk and Dove and were no selling attacks.

Defeats 3 Agents in 10 Seconds.

Easily out-skills the Parents of the Nuclear Family, the only reason he lost was due to their superior physicals.

Beats a dozen Guards while drugged.

Disarms a thug in a Second.

Stomps 2 guys.

After one of the guys (in the above link) gets back up, Robin smashes him through a Wooden Pallet.

Season 2:

Stomps Jason Todd, 2.

Displays some good skills in a training session (Dick is teaching the other Titans).

Bests Rose Wilson in a spar multiple times.

Takes down 5 Prison Guards in seconds.

Becoming Nightwing:

During his transformation to Nightwing in 2x11, we see a clear improvement in his fighting ability, during his hallucination fight against Bruce Wayne, as the fight starts, he gets dominated for the first 90 seconds, casually at that, with Bruce not getting tagged a single time. After this, Dick miracoulosly gets a skill boost, and is able to trade evenly, with neither Bruce or Dick landing a hit.

Not Robin anymore... faster... stronger... like a Bird of Prey

- Bruce Wayne

Lasts about 90 seconds about Deathstroke, though Slade didn't seem to be fighting as smart as he was at the end, as he was angry due to Dick constantly mentioning Jericho.