Current boost converter solution for: 1.8~5V input and 15W output (12V, 1.25A)?

Hello every one,

I am a current boost converter with the input variation from 1.8 to 5 V and the fix output for 15W load (12 V, 1.25 A). I am using combination of TPS61220 (http://www.ti.com/product/TPS61220) for the first stage and TPS61088 (http://www.ti.com/product/TPS61088) for seccond stage (similar to there combination: http://www.ti.com/tool/PMP9772. But when the input voltage reduce below 3.4V the output voltage and current begins droping.

I think TPS61088 is not efficient enough? 

Anyone has recommendation?

Best regards,

Nga