However, in some cases, there are tasks that do not contribute to achieving goals but do require immediate attention and you simply cannot delegate it to others. How do you address / prioritize this using Eisenhower Marix?
In reply to your question, it's important to remember that the Eisenhower Matrix is a guideline to help you prioritise your tasks in the most productive way. Delegation isn't always something that your boss asks you to do - it can be you asking a friend or a family member to handle something for you.
If there's absolutely no way it can be delegated, then naturally the responsibility to complete the task falls on you. All the Matrix does is highlight the fact that your time would be spent more productively on tasks in the first two quadrants. It's down to your best judgement and analysis of your time and workload in conjunction with the use of the Matrix to decide whether you take it on yourself or delegate it.