Can Penguin Soldier Return Itself When Attacked?

If Penguin Soldier is attacked, its Flip effect activates After Damage Calculation. If Penguin Soldier was determined to be destroyed by battle, you cannot target it using its own Flip effect, as you cannot return determined-to-be-destroyed monsters to the hand or deck.

Does Penguin soldier die when attacked?

(Since "Penguin Soldier" was destroyed by battle, you cannot target itself.) After the effect of "Penguin Soldier" resolves, if "D.D. Warrior" was returned to the hand, "Penguin Soldier" is still banished.

Can Penguin Soldier return itself?

If your "Penguin Soldier" is not destroyed when its Flip Effect activates, you can use it to return this card itself to your hand along with one other monster.