What is 깨긴깼다?

Question

What is 깨긴깼다?

Answer

-긴 is a abbreviation of -기는

From http://www.talktomeinkorean.com/lessons/l6l24/

The key is “-기는”. This is the noun form -기 plus the topic marker -는. The topic marker is used to show contrast.

Example #1
갔어요. = I went (there).
→ 가기는 갔어요.  = I DID go (there) but...
→ 가기는 했어요.  = I DID go (there) but...
→ 가기는 갔는데, 일찍 왔어요.  = I DID go there, but I came back early.
→ 가기는 갈 거예요.  = I WILL go, but … ( + other premises )

Example #2
봤어요.  = I saw (it).
→ 보기는 봤어요.  = I DID see (it) but ...
→ 보기는 했어요.  = I DID see (it) but …
→ 보기는 봤는데 기억이 안 나요.  = I DID see it, but I don’t remember.

깨다 means "break ; wake up"
But it also means "pass every level of the game".
(게임을) 깨긴 깼다 means "I passed every level of the game, but..."

깨긴 깼다 can have other meanings depending on the context.
I woke up, but...
I broke it, but...