Damien Reeves broke the deadlock by finishing via the crossbar from James Lawrie's cross before Josh Ginnelley doubled the lead after a 50-yard run.
Jake Moult ended the game as a contest, converting a penalty after the lively Lawrie was fouled by Omar Beckles.
And Jordan Sinnott completed the Shots' miserable afternoon, scoring after good work from Ginnelly.
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Aldershot Town boss Barry Smith told BBC Surrey: "We didn't defend properly and their front four caused us so many problems.
"It was down to us not defending properly for the first goal. It comes from a centre-back not being dominate and we couldn't get a grip in the game.
"We lost battles all over the park today. Once you cross that white line it is down to the players to make sure they are doing the jobs that they've been asked."
Altrincham moved out of the National League relegation zone with an impressive victory over Aldershot.