Most phones can capture a whole chat, receipt or web page as one tall image. Take it with the steps for your phone below, then drop it into the tool above: it cuts the image into A4 pages between lines of text, so nothing is sliced in half.
Open the chat and scroll up to the first message you want. Take a scrolling screenshot with your phone's steps above; for a long conversation take several, each starting where the last one ended. Add them all here — they are stacked in the order you add them, and you can move any of them up or down before you make the PDF.
WhatsApp's own Export chat gives a text file, without the look of the chat. Use screenshots when you need the conversation as it appeared on screen — for a complaint, a police report or a bank. Nothing you add here is uploaded.