A beer milkshake is a special type of milkshake invented by Dave Lister.
In basics, it is a milkshake that tastes like beer, but it is never revealed how (it is probably just a milkshake with beer poured on it). It is not known whether or not it is a truly alcoholic beverage. Lister has taught at least one of the Red Dwarf vending machines how to create it. (RD: Waiting For God)
It is mentioned several times in Series I. Confidence listed it as one of Lister's greatest inventions with the quote "another great idea from the people who brought you beer milkshakes!" (RD: Confidence and Paranoia)