Finding the Length of the shortest Accepting path of a NDTM
Your problem is $\mathsf{NP}$-complete, and you can find a proof for instance here (I gave a sketch in comments). 

A remark: If you consider $\{\langle M,x,t\rangle : M$ halts on $x$ in $t$ steps $\}$, then you can only show it is $\mathsf{NP}$-hard. But as you mention that you consider $t$ polynomially bounded (in the sizes of $M$ and $x$, I guess), then your problem belongs to $\mathsf{NP}$.