TI LM25118 buck boost, variable power supply
There's nothing technically stopping you from drawing 1A from this supply if your source is able to source that much power, and you take efficiency into account, and of course if you designed the inductor, switch and smoothing capacitors accordingly (which you can do by using TI's own supply designer tool on their website, so I assume you did that and will choose proper components by simply following its design).

So, the max input power is 3V · 4A = 12W. Your max output power is 12 V · 1A = 12 W. That can't work with any supply, doesn't matter which because there's no such thing as a 100% efficient power supply. 

So, get a beefier input, or reduce your output requirements.

Note that it's not easy to operate a buck-boost supply at \$V_\text{in}\approx V_\text{out}\$; if that is among your requirements, more involved architectures like Cuk or SEPIC might be better suited.