The first burrow run level (in the first hub, Sky Castle) unlocks along with level #4 Piggy Peril after beating level #3 Lord Ember's Domain and is located on the ridge above Piggy Peril.
It's a very simple, easy level with only one spot, I think, where you could die besides taking damage from running into enemies. It's an auto-run side scrolling level with a variant orientation where you decide whether to burrow or run.
Use the jump out of burrow mechanic or fall at a sharper angle mechanic into a burrow to collect coins, avoid enemies and obstacles, and reach the clover at the end.