You don't say what operating system or browser you are using, so I can't be specific. An alternative to taking several screenshots and stitching them together would be to print the entire web-page to a virtual printer driver as a pdf. This would give you a single pdf file containing the entire conversation (assuming you can display them all at once). There are free pdf printer drivers for all major operating systems.

The most important thing to check would be with your lawyer as to what format was acceptable to them and/or the courts.

In a situation, where a law suit is being handled, and I need to get all the messages from a conversation I had online. I need to have a screen shot of the whole conversation. There are over 1,000 messages, so it would take a long time, doing one screen at a time. How do I get a screen shot of the whole page, with out having to do one screen at a time?