That Electra who gets an attack that is equal to its defender.

Is that constantly changing if they put an acro dodge on the defender or will it only check on legality of attack.

It only checks at the beginning of the attack.

so someone can use acro dodge to increase defense

I guess you should read it "When Elektra becomes an attacker she gets +X where X equals the defenders defence."

now is the attack level checked when legal--

reads

"Whenever Elektra attacks, she gets +X ATK this attack, where X is the DEF of the defender"

Or would it change with the changing defense.

It DOES NOT change with defense boosts. It goes off when the attack begins, and is than set.

Of course, you can change it with plot twists during the attack.

To be more precise, when Elektra becomes an attacker, an effect goes on the chain that says 'Elektra gains ATK equal to the DEF of defender'. Until that effect resolves, any DEF boosts on the part of the defender will be added to Elektra's ATK as well. (most players will choose to pass to let that effect resolve and then boost DEF). Any DEF modifiers after Elektra's effect resolves will not increase Elektra's ATK.