This is not by me! It is a friend's answer which helped me to get it an easy way :
아직 mainly means 'yet'.
I'm not ready yet.
나는 아직 준비가 안됐어요.
아직도 mainly means 'still' but can be used as 'yet' and it has a bit emphsis.
"It's still raining."
"아직도 비가 와요."
"I'm not ready yet."
"나는 아직 준비가 안됐어요."
This is a normal statement, it only conveys the information that the speaker is not ready. There is no implication.
"나는 아직도 준비가 안됐어요."
This sentence, whereas, tells the situation depending on the context.
So it can emphsize the situation that the speaker is not ready.
Let me give you an instance.
"Have you dicided?"
결정했어요?
"No, I don't know."
아니, 모르겠어요
"Why are you so indecisive?"
왜 그렇게 결정을 못해요?
"I don't know. I'm not ready yet."
모르겠어요, 아직도 준비가 안됐어요.
Another instance.
"It's raining."
"비오네요."
"still?"
"아직도요?"
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저는 아직도 너무 지루해요(sounds natural)
저는 아직 너무 지루해요.(sounds awkward)
아직도 -(has an ehmpasis) still, yet
아직 - yet
This is very hard to explain because it's about the nuance.
I think it takes time to understand.
Hope I could help a little. ^^