As lawyers jockey for the lucrative job of overseeing Herbalife Ltd.’s compliance with the terms of a $200 million settlement, top firms are giving a glimpse into their billing rates and revealing strategies for winning coveted independent-auditor contracts.

The Federal Trade Commission last week received more than two dozen applications from law firms, financial companies and other businesses vying to ensure the Los Angeles marketing company complies with its deal to resolve consumer-deception charges.