jmc

It doesn't matter the order in which we add and subtract values, but we'll start with $2122_3-2111_3$ since the values are close. \begin{array}{c@{}c@{\;}c@{}c@{}c@{}c} & & 2& 1 & 2 & 2_3\\ &- & 2 & 1 & 1 & 1_3\\ \cline{2-6} & & & & 1 & 1_3\\ \end{array}Now we're left with $121_3-1200_3+11_3$. We add $121_3+11_3$. \begin{array}{c@{}c@{\;}c@{}c@{}c@{}c} & & & 1 & 2 & 1_3\\ &+ & & & 1 & 1_3\\ \cline{2-6} & & & 2 & 0 & 2_3\\ \end{array}So we have $202_3-1200_3=-(1200_3-202_3)$. \begin{array}{c@{}c@{\;}c@{}c@{}c@{}c} & & 1 & 2 & 0 & 0_3\\ &-& & 2 & 0 & 2_3\\ \cline{2-6} & & & 2 & 2 & 1_3\\ \end{array}Our answer is $\boxed{-221_3}$.