Looks like a support setting issue. What were your print settings and filament type?
Regural speed, pla, with support from anycubic app slicer
TBH I've never had much luck with the anycubic slicer and I just use Cura. For this model with PLA, with what I can see, I would print at 0.42mm line width (assuming 0.4mm nozzle) 0.2mm layer height, 3 walls, 4 top/bottom layers, outside to inside, 15% infill in grid and connect infill lines, 80-100mms, 205°, 60° bed, -0.3mm initial layer expansion (remove the elephant foot), normal support at 15% density and zigzag pattern with 0.16mm support Z distance with disabled support interface, 1.0mm retract at 40mms and 25mms prime speed with retract before outer walls and on layer change, combing set to infill only. You could also edit the model so that the unsupported part on top is moved back to be flush with the bed or thicken it so that the whole model is an equal height but obviously that may not be the look you're going for.
As a final option you could also print in two sections with a pin and hole to join later, but many don't want to glue and deal with post processing though. I've found many models actually print faster and better in multiple parts that are joined later. Doing this would eliminate the need for supports and you should be able to print both at the same time.