Whether you need underpinning I cannot tell you. We have one at the old retaining wall in the area of the house. It was determined back then by the structural engineer, expert, and the construction contractor.
Work was done in 1.5-meter increments. 1.5 m excavated and concreted, 3 m left standing, 1.5 m excavated, and so on. A few days later the next 1.5 m, and a few days later the rest. Roughly took about 2 weeks.