What is the skill of trying the best to finish a hard task assigned? While having impediments on the way, without complaining, exploring solutions and putting in practice till the end.
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I think you want assiduous. The OED says:
Generally I hear such people referred to as having great focus.
Another term you hear a lot is dogged (typically pronounced almost like it is two words: dog ed). The word dog is sometimes used in English as a verb to describe the act of persistently chasing after someone or something. Dogged can be used as an adjective, and occasionally doggedly as an adverb.
In a more ambivalent sense, sometimes we use the metaphor or simile of a bulldog ("He's a bulldog"). This is an animal that is somewhat famous for refusing to let go of something it has bitten down on, even when you want it to.