Drink like a fish
Drink heavily, especially of alcoholic drink.
Clearly an allusion to fishes' close association with water and their apparent open-mouthed taking in of water. Freshwater fish actually take in water by absorption rather than by drinking, although sea fish do actively drink seawater.
Sea fish do actually drink seawater - don't try this at home.
The phrase is known since 1640 and appears in Fletcher and Shirley's The night-walker, or the little theife, from that date:
"Give me the bottle, I can drink like a Fish now, like an Elephant."
'Drink like an elephant' didn't catch on. There is a more recent potential boost to use 'drink like a fish' - at least for Californian Valley girls. In January 2005 a press release for the Dalian Fisherman's Song Maritime Biological Brewery in China, said that they had developed a fermentation process to make fish into wine. So now, you can 'drink, like, a fish'.