HUGE plot hole

okay, now The Penguin attempts to threaten Supergirl with a bomb made with what i'm assuming is conventional explosive materials (i.e. TNT, RDX, ammonium nitrate)... HOWEVER, would not Supergirl - a daughter of Krypton - have absolutely NOTHING AT ALL to fear from the results of said bombs detonation? is not Supergirl essentially invulnerable to even the most extreme acts of violence imaginable?? i thought only KRYPTONITE (and other, weirder comic book variations) could harm Earth-based Kryptonians?

i mean... this is KIND of basic stuff here! it's ALMOST as if the makers of this film didn't CARE about such obvious logistical problems! it's ALMOST as if the makers of this film weren't paying attention to such glaring, script-level issues! it's ALMOST as if the makers of this film were total fraud ####ing hacks just BARELY capable of intelligent thought, reasoning and/or basic motor skills!

almost!