When Orcish Bowmasters enters the battlefield, it triggers, creating a 0/0 Orc Army token if you do not control an Army, then putting a +1/+1 counter on an Army you control and dealing 1 damage to any target.
Activate the Orc Army using Whirlpool Warrior's ability by paying ({1} magic symbol) and sacrificing it, causing each player to shuffle their hand into their library, and causing each player to draw that many cards.
Orcish Bowmasters triggers for each card opponents draw this way.
Resolve the first trigger, creating a 0/0 Orc Army token, then putting a +1/+1 counter on it and dealing 1 damage to any target.
Activate Phyrexian Altar by sacrificing the Orc Army, adding ({1} magic symbol) .
Resolve the second Orcish Bowmaster trigger, creating a 0/0 Orc Army token, then putting a +1/+1 counter on it and dealing 1 damage to any target.
Holding priority, repeat from step 3 an arbitrarily large number of times.
Resolve the first remaining Orcish Bowmasters trigger, if applicable, creating a 0/0 Orc Army token if you do not control one, then putting a +1/+1 counter on an Army you control and dealing 1 damage to any target.