multi strike
You'd ideally (not!), want to hit a flock of Gulls or some Canada Geese for some damage like that. Depending on the altitude of yourstrike and one engine still giving some power, one assumes you may have departed the airport by a few minutes or so, as they don't return immediately, so you'll need some birds know for @rsing around at altitude!
Try these for size, both copyright from 'Sharing the Skies'.
The first apart from being a turboprop, nearly meets your requirements to the letter in your 'storyboard',
On October 4th, 1960, a Lockheed Electra encountered a flock of European Starlings just after becoming airborne from Boston’s Logan International Airport. Starlings fly in dense flocks of individual birds weighing about 80 grams each. Numerous birds were ingested into three of the four turboprop engines. The number-one engine had to be shut down; numbers two and four lost power. The aircraft lost speed, stalled and crashed into Boston Harbor. Of the 72 persons on board, 62 died and 9 were injured.
On the night of January 9th, 1998, a Delta Airlines B727 departed Houston, Texas. At about 6,000 feet the aircraft struck a flock of migrating Snow Geese and suffered extensive damage to all three engines, the leading edge slats, the radome and the airspeed pitot tube—damage due in part to the aircraft’s involvement in a trial to assess the efficiency gains of high-speed departures. The crew successfully returned to the airport and there were no injuries. An FAA search will bring the full reports up no doubt, but the aircrew here could maybe put that into a 757 context, which I too would be interested to read!