This page of the Cyberpunk 2077 tutorial contains a detailed walkthrough description of the Small Man, Big Mouth quest.
This mission is available only for Streetkid V. Kirk, one of the Night City fixers, calls V to offer them a job. He wants to meet in El Coyote Cojo. Accept the invitation and go to the bar to meet with Kirk.
Meet with Kirk at El Coyote Cojo
Kirk is interested in the things located in the van parked in the Valentinos gang territory. Your task will be to retrieve the combat cyberware hidden in the tub and deliver them to the fixer. Go to the location designated by Kirk.
Defeat the Guards
The van is in a nearby garage, but the area is swarming with Valentinos thugs. You can get inside in a few different ways: through the parking lot (2 enemies outside) or by jumping over the fence on the left (unguarded side of the building).
You can act quietly and eliminate the gang members one by one, or use your favorite type of weapon - the choice is yours. If you want to use a sniper rifle, you will find a convenient shooting position on the garage roof.
See what's inside the truck
When you deal with all your enemies, enter the garage and open the back of the van. Inside, instead of the promised combat cyberware, you will find cheap fake clothes - Kirk was not very well informed. Go confront the fixer.
Return to Kirk
Kirk was not very lucky and fell into the hands of Valentinos. The gangsters admit that they gave him false info to get rid of the fixer. You can avoid fighting these enemies, if you allow them to humiliate you.
Otherwise, you will face a heavy battle with well-armed thugs. If you want to fight, aim at the head to get rid of at least one of your opponents as soon as possible. Then, hide behind an obstacle and finish off the other enemies. As a reward for completing this quest, you will receive a considerable number of experience points.