Legally valid. The plastic surgery hospital has signed with you the equivalent of an installment sale contract, which is in accordance with the law.
According to Article 634 of the Civil Code, if the buyer of an installment payment fails to pay the price due in an amount of one-fifth of the full price, and after a reminder fails to pay the price due within a reasonable period of time, the seller may request the buyer to pay the full price or terminate the contract.