The greatest power among other creatures you control is determined as the boast ability resolves. You choose at that time whether you'd like to change Arni Brokenbrow's base power. If you control no other creatures at that time, you can change Arni's base power to 1 until end of turn. Arni objects to this course of action.

Arni Brokenbrow's new base power is set to the 1 plus the actual power of the other creature you control with the highest power, not that creature's base power. If that creature's power changes after the boast ability has resolved, Arni's power is unaffected.

If a creature with a boast ability is put onto the battlefield attacking, it was never declared as an attacker. Its boast ability can't be activated that turn.

In some unfortunate cases, the greatest power among other creatures you control may be negative. For example, if that greatest power is -3, you could change Arni's base power to -2 until end of turn. Arni strenuously objects to this course of action.

A boast ability can be activated at any point after the creature with that ability has been declared as an attacker. This can be before blockers are declared, after blockers are declared but before combat damage is dealt, during combat after combat damage is dealt, during the postcombat main phase, during the end step, or, in some unusual cases, during the cleanup step.

If it's not your turn and you gain control of a creature with a boast ability after that creature attacked, you can activate that creature's boast ability if it hasn't been activated yet that turn.

Any effects that modify Arni Brokenbrow's power without setting it to a specific value will apply after Arni's base power is set, regardless of the order in which those effects were created. The same is true of counters that modify Arni's power.

If an effect adds additional combat phases to a turn and a creature with a boast ability attacks more than once during that turn, its boast ability can still be activated only once.