Learn Turkish: Hedeflediği başarı için gözünü kırpmaksızın çalıştı. - He studied without blinking an eye for the success he aimed for.

The ending -maksızın is the formal negative converb taught in this lesson. Attached to the verb stem kırp- (to blink), it means 'without blinking'. You absolutely could use kırpmadan here instead; they mean the exact same thing, but -maksızın gives the sentence a much more formal or literary tone.

What is the grammar behind hedeflediği?

It is an object relative clause using the -dik participle. It combines the verb hedefle- (to aim or target), the participle -dik, and the 3rd person possessive ending -i, which causes the k to soften to ğ. Together, hedeflediği başarı translates to 'the success that he aimed for'.

Why does gözünü have two -ü endings separated by an -n-?

The first -ü is the 3rd person possessive suffix, making it 'his eye'. The second -ü is the accusative case marker, because his eye is the direct object being acted upon by the verb kırp-. Whenever you attach a case marker to a 3rd person possessive ending, Turkish requires the buffer consonant -n- between them, resulting in göz-ü-n-ü.

Is gözünü kırpmaksızın a standard idiom?