I'm going to work hard so there's nothing left undone.

Literal

Left-undone thing [subject-が] not-exist [purpose-ように] work-hard [emphatic-ぞ].

やり残す ('to leave undone') is a compound: やる 'to do' + 残す 'to leave behind.' ように ('so that') sets the goal. 頑張るぞ is a masculine self-motivating declaration. The sentence expresses determined resolve to see things through completely.