Using highest Sauté function, heat oil in Instant Pot until shimmering. Add asparagus, bell pepper, and shallots; cook until softened, about 5 minutes. Turn off Instant Pot and transfer vegetables to bowl. Stir in goat cheese, tarragon, and lemon zest.
Arrange trivet included with Instant Pot in base of now-empty insert and add 1 cup water. Spray four 6 ounce ramekins with vegetable oil spray. Beat eggs, 1/4 cup water, and salt in large bowl until thoroughly combined. Divide vegetable mixture between prepared ramekins, then pour egg mixture over top (you may have some left over). Set ramekins on trivet. Lock lid in place and close pressure release valve. Select Pressure Cook function and cook for 10 minutes.
Turn off Instant Pot and quick-release pressure. Carefully remove lid, allowing steam to escape away from you. Using tongs, transfer ramekins to wire rack and let cool slightly. Run paring knife around inside edge of ramekins to loosen frittatas, then invert onto individual serving plates. Serve.