\begin{equation} \begin{split} 1000&=(8+8)\times 8\times \sqrt{8\times 8}-8-8-8\\\ &=8\times 8\times8\times\sqrt{\sqrt{8+8}}-8-8-8\\\ &=88\times 88\div 8+8\times \sqrt{8+8}\\\ \end{split} \end{equation}
If allowed to use exponents, another solution is:
$$1000=(8+(8+8)\div8)^{\sqrt{\sqrt{8+8}}+8\div8}$$