Approach the second sun with an odd stack

I have an odd question with the stack. I just ended a commander game and im curious of this was a legal action

I had Jin-Gitaxias progress tyrant on the board which copies a spell and recast it. It also counters the first instant/sorc/artifact played during that turn. Here's how the stack looked

I cast Approach the second sun

Jin Gitaxias copied it

Casting a 2nd approach the second sun (This doesn't win me the game, simply gives me the 7 life)

Somebody played an instant which Jin counters automatically

Then a fierce guardianship is put on the stack targeting the first card on the stack (Approach the second sun)

Can a card target that deep into the stack countering my initial Approach the second sun?