Have "The Wicked Avatar" in your control along with this card to ensure that there is a monster with the highest ATK. This monster's effect is a Quick Effect, which applies during the Damage Step whereas the effect of "Wicked Avatar" is continuous. This should mean that when "Timaeus" is attacked and its effect activates, "Wicked Avatar" should be selected (not targeted) and would have 100 more ATK than whichever other monster(s) would have the most at the time. Then this card's effect would resolve and move on to damage calculation while the ATK of "Avatar" would instantly change to be 100 ATK more than "Timaeus". The ATK of "Timaeus" would remain at this value until it is attacked and its controller decides its effect should be triggered again. This way your opponent can't destroy this monster in battle with a draw (unless they have a "Wicked Avatar" of their own).
Combo with "Mound of the Bound Creator". Even though this card will be unaffected by it, 1000 damage will still be inflicted if this card destroys a monster by battle.