I agree with red_pill that the starting point is to declutter the obligations, reduce the inputs, and feel the joy of saying "no". None of us can do it "all" whatever that is, and most of us can realistically only do "some". One way to handle the overwhelmed feeling:
1. do a "dump" of all the should do's that are weighing on you in order to capture everything
(this is core Getting Things Done territory)
2. separate them on the Time Management Grid -
https://www2.usgs.gov/humancapital/documents/TimeManagementGrid.pdf(popularized by Covey)
3. focus your energies on Q1 Important & Urgent activities to clear the decks
Edited: if everything seems Urgent & Important to you, rank the activities in this Q. Figuring out your ranking order will be illuminating. Since you can't do everything, better figure out which things are really at the top. Pro tip - the answer isn't "everything". What is really important to you and why?
4. make sure to block time for Q2 - Not Urgent & Important - high value activities; this is where you want to spend most of your time eventually
5. pretty much ignore Q3 and Q4 - Q4 is very seductive as easy "wins" are here
6. review your lists in each Q periodically to make sure activities are still in the right Q - or should be removed entirely
(regular review is a GTD cornerstone for peace of mind)
7. do regular dumps to make sure you're capturing anything that's weighing on you
8. reduce the amount of things you're trying to pay attention to or accomplish. Less is more.
And from the MMM archives -
http://www.mrmoneymustache.com/2016/07/13/making-space-for-badassity