He had to work very hard to make his story hold together.
Tips
usage
自圆其说 often carries a slightly negative connotation - the person is straining to make their account fit, patching holes in their story. It doesn't necessarily imply lying, but does suggest the original claim was flawed.
memory
圆 (yuán) means round/complete - imagine rounding off all the rough edges of a story until it makes a perfect circle with no gaps.
