For those wondering. I believe this is from season 1, episode 1 of the TMNT. By the time this scene happens they have met April and she wants to take them to the surface to help her investigate a spree of "high-tech industry robberies." She wants to break the case because up until now, she had been stuck "reporting on fashion shows" which is beneath the young 23 year old's ambitions as a journalist. She hands out the trench coats and hats, after which Rafael does an impression of Humphrey Bogart and says "here's lookin' at you, sweetheart." She calls the turtles by the wrong name and they correct her. This is so that the audience can hear the turtles say their names so they can identify and become familiar with them (though in this episode there are a few instances of turtles speaking with each others voices.)

After they get the costumes, they go about the streets of NYC in a comical "fish-out-of-water" sequence--for instance, a street hustler playing three card monty asks Leonardo to cut the cards, in which he takes out his sword and 'cuts' the table in two.

They venture into what I can only describe as the 'ninja district' of Manhattan. This includes everything from Ninja Pizza to Ninja Dentist (Donatello comments: "Ninja Dentist? Ouch!"). They enter the ninja pizza ("home of the nice slice"). Which is really a front for the footclan. For some reason April walks off while they are eating pizzas with odd toppings because she needs to use a pay phone. She is kidnapped.

The turtles track her to a tall building and confront the foot soldiers on the roof. At the beginning of the fight one of the turtles knock down a foot soldier and the sound he makes indicates these are robots, not people (Raphael says "Clang? Did you say clang?!?!?").

After this revelation the turtles know they can trash these guys without killing anyone. The turtles take off the trench coats and hats because they wont be discovered. Michelangelo says, "All right, LETS PARTYYYYYY" and jumps from behind the door entrance on the roof to battle them. The TMNT theme music starts up and for the first time we see the turtles in their pure ninja glory.

They defeat the foot soldiers and try to head out of the building. However, a voice over the loud speaker repeats "All Foot return to the Technodrome." This is the voice of Shredder. They wonder what the Technodrome is. Donatello comments that he doesnt know but it can only be one way, "DOWN!" As they head down to the basement the building is flooded. They escape back to the roof and swing over to another building on an ersatz zip line made of rope and Leonardo's sword.

After they are safe, the building bursts in a deluge of water (ostensibly killing a lot of people I assume, this is never addressed or even spoken of ever again).

They are back at the lair. April says she finds it unbelievable that she is now friends with "half teenagers and half turtles" (which doesnt make a lot of sense because teenager is an age and turtle is a species. Like there could still be a youthful turtle without it being a mutant ninja turtle, ya know). Then the episode fades out with discussion of gross pizza.

If anyone has any questions about the first episode, please let me know.

TL/DR: HEROES IN A HALF SHELL, TURTLE POWER.

Source: Watched this episode about 500 times with my son because the re-released action figures came with the first episode on DVD.