How high does your heart rate need to be before you get a heart attack?

Varies: If you have normal arteries, no heart rate will cause a myocardial infarction ("heart attack") but rare conditions (wpw etc) can cause very rapid heart rates (eg > 220) that will pump ineffectively because of inadequate filling time. If there's blockage, the hr that is harmful (by increasing myocardial oxygen consumption) will depend on severity and location, age, contractility, and wall stress.

Depends: Depends on pre existing coronary artery insufficiency status, age, pre existing co morbidities, anemia, altitude, state of hydration, pulmonary status, presence of valvular pathology, type of rythm to include some. Therefore there is not a majic number that applies to all, it is specific for each heart particular situation.

Not related: A heart attack can occur at any heart rate if there is a blood clot in the artery or a blockage. If there is a severe narrowing than a higher heart rate will increase the risk of a heart attack as the demand of a higher heart rate would out strip the supply.