累坏 is a 'verb + result complement' - 累 ('tired') + 坏 ('to the point of breaking'). It almost always pairs with 了 (le): 累坏了, meaning the exhaustion has actually happened. Same pattern as 气坏了 ('furious'), 笑坏了 ('laughed to pieces').
mistakes
累 has two tones: lèi (tired, this word) vs. lěi (to accumulate, as in 积累). Don't mix them up - different word, different pronunciation.
