Spend all of the beginning 500 gold into swords fast and get miners.
Gradually build your army to at least 6 swords, and 3-4 miners (hopefully a few archers) then charge/
Elemental has strong but expensive and time-consuming unit training and your massing of a high-damage unit can wreck him early on.
Attack (but grab the center first). If he has Charrog, kill that first (but get your archers past it to attack anything else)
If he has an air unit, make that a kill priority too, and especially the miners. If his air unit goes to attack your statue, you win because your army will have a far larger health pool and attack damage (and you will probably have enough money for a castle archer and walls by then)
If he has a Castle Air Elemental, your army is screwed if you stay but use your archers to either kill them where they stand or drag them out.
(I've won 3 of 5 of my vs. Elemental games this way)