Choosing inductor and capacitor for boost converter
The TPS613221A has a typical switch current limit of 1.2 A, and the guaranteed minimum is 0.75 A. Anyway, the maximum output current is different (as shown by formula (1)).

At least for an inductor of 2.2 µA, trying to get 1.3 A out of it would be a bad idea:



You need a more powerful boost converter, like the TPS61021A:



And putting your requirements (1.6­–3.1 V, 3.3 V, 1.3 A) into TI's Webench tool indeed results in a design based on the TPS61021A, with a 1 µH inductor (SRU1028-1R0Y), and 10/30 µF capacitors: