PerformanceGoal option ignored in V11.1

The quick fix

is to use Block:

Animate[
   Block[{$PerformanceGoal = "Quality"}
     , Plot3D[Sin[t x y], {x, -3, 3}, {y, -3, 3}
         , PlotRange -> {0, 1.2}
       ]
   ]
 , {t, 0, 2}
 , AnimationRunning -> False
 , DisplayAllSteps -> True
]

fyi, This has been fixed in 11.2. Tested it on the cloud under Linux