What incident sparks the conflict in the mariner`s story?what inciden servers as the climax?

The incident that sparks the conflict is when the Mariner kills the albatross. This beautiful bird that guides them out of the ice and into open water was considered a "good omen" by sea-faring men. The Mariners transformation occurs when he realizes the wonder of all God’s creatures,

“The great water snakes moved through the silvery moonlight, glittering; blue, green, and black, the snakes coiled and swam and became beautiful in the Mariner’s eyes. He blessed the beautiful creatures in his heart.”

Yes, he even likes the slimy sea snakes. The albatross falls off his neck and sinks into the ocean.