I would highly recommend printing this with ABS or Taulman's 618 Nylon, as PLA's lower glass-transition temperature (60-65 degrees C) will easily be reached during a dishwasher cycle.

Print with the smallest side up, the internal overhang angles are small enough to not need any supports. If you are printing with a raft, use a heatgun on the underside where the raft detaches. This will get rid of the lighter-coloured "stressed" plastic and help make the part water-tight.

I would like to stress that although this part functions as a beverage container, don't use it as one unless you have considered the safety of using 3D-printed foodware. The common plastics used in printing, ABS and PLA, have certain grades that are considered foodsafe. HOWEVER, running ANY form of plastic through a 3D printer will introduce oils and other volatiles into the plastic. In addition, the cavities within a printed part (even one with 100% infill) will never be fully cleaned (by hand or in a dishwasher).

It boils down to this: use this to hold beverages if you have considered the risks and judged them worth it.