The Persian army of the Achaemenid period never used elephants. There is no evidence of elepants being fielded by the Persians in any of the battles against Alexander, or in any battles before that time.
The only time Alexander faced enemy elephants was at the battle of the Hydaspes (326 BC) against the Indian king Poros. He does not appear to have had any plan to deal with them. Poros deployed his elephants along his centre, where they confronted the Macedonian pike phalanx. When the elephants charged his infantry, Alexander was busy elsewhere, attempting to drive off Poros' cavalry on the flanks. The pikemen did what they could to cut down the beasts while their light infantry support targeted the riders. The elephants inflicted heavy casualties but were eventually driven back into their own lines.
Elephants only seem to have made it into the warfare of peoples further west a generation later, when the deal Seleukos made with Chandragupta Maurya secured 500 war elephants for his army.