I cannot give you a very specific answer without knowing more about your XML and what kind of panels you use.
For now, here is a generic approach that you can play with.
Add the following to your dashboard SimpleXML just before the closing </form> or </dashboard>. Getting the vertical scrollbar to appear relies on limiting the height of the panel and turning overflow to auto. The following will set the same height limits to all panels. You can change the value of the max-height setting to increase or shrink the panels. If you need to set the limits different for certain panels, then you will have to identify the panels by an ID and reference that ID in the CSS setting.
<row depends="$dont_show$">
<panel>
<html>
<style>
.dashboard-row .dashboard-panel .panel-element-row {
overflow: auto;
max-height: 200px;
}
</style>
</html>
</panel>
</row>
