If this card destroys an opponent's monster by battle: Your opponent skips their next Main Phase 1.
Rulings
Individual Card FAQs
If your Main Phase 1 is skipped because of "Timeater", you can enter your Battle Phase (even if you have no monsters on the field) and proceed from there to Main Phase 2. If you cannot enter your Battle Phase (due to another card effect such as "Great Long Nose" or "Frozen Soul"), then you must go immediately from Standby Phase to End Phase.
If your "Timeater" and your opponent's monster destroy each other as a result of battle, the effect of "Timeater" is still activated.
DARK|
Level 6|[ Machine / Effect ]
ATK 1900|
DEF 1700