any ideas on how to export the all Activity History for every lead in your lead database or leads from smart list using SOAP API? Support team wasn't able to help me with it as well as the professional services team.
You'll want to use getLeadChanges for this. You can set a specific timeframe for activities, and then page through all of the results for that timeframe. Once this is complete, you can push the timeframe forward and then page through that until you've grabbed all of your lead activity.
I'm not claiming to be an expert here (in fact, I haven't built out any APIs). But looking around at this issue myself, I did find this for "getLeadChanges" documentation. getLeadChanges » Marketo Developers