僕は今度の日曜日は勤務だ。

。

I'm on duty this coming Sunday.

Literal

I [topic-は] this-coming [possessive-の] Sunday [contrast-は] duty.

今度の ('this coming, next') marks the upcoming instance. 勤務 (きんむ, 'duty, work shift'). Double は: 僕は (topic) and 日曜日は (contrastive — singling out Sunday).