Mail attachments are individually saved using the Mail Action Menu; simply touch-and-hold the attachment’s icon to expose the Action Menu, then select Save to Files. You can also directly drag-and-drop the attachment icon from the Mail to a folder in the Files App; unless you are well practiced, using split screen (with Mail and Files windows) might be the easiest method for this technique.
Drag-and-drop supports multi-select - and this may simplify saving multiple items in a single action. To use multi-select, touch and move the first attachment icon; a green “+” badge should appear. Without lifting you finger from the screen, tap on each additional attachment icon to add to the stack. When you have selected all the icons, drag the stack to the target folder.
The multi-tasking and multi-select tools enable considerable flexibility in selecting and moving items around the UI.