You can help him a lot - but perhaps not 100%. I see two major ways of doing this:
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the Asana-recommended way - he allows you to edit My Tasks (by Sharing it). You will not see all his tasks - only those he adds to a Project you have access to, or makes you a Collaborator on.
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my suggestion - create a Project called “Boss’s Tasks”, where you are also a member, and also help him create and save a report he can view frequently, that searches for tasks assigned to him that AREN’T in “Boss’s Tasks”. He then would need to add them. (He can avoid adding any task related to you.)
Both require some help from him. Good luck!
(BUT: The actual work of setting up and using Asana is not hard per se. The thing that may make it time-consuming is all the thinking, connecting the dots, prioritizing etc. that goes along with this. If you can do that for him, this may work - otherwise, I fear any tasks in Asana will become obsolete shortly.)