Can I get 12V out of a 3.6V battery
The listing says it takes 0.4A/meter @ 12v, which is 2A since the strip is 5m long; but elsewhere it says it takes 48W/5m which would be 4A.  I'll err on the high side and use the 4A figure.  That's 137 mA per LED since there are 300 LEDs, which seems reasonable for superbight LEDs.

You're not going to find a boost converter that can handle 4A.  Plus, that would mean you would be drawing around 16A from your battery:

$$\frac{\frac{12v}{3.6v}*\times 4A}{0.85} = 15.6A$$

where the 0.85 represents 85% efficiency.

With one 1300 mAh 3.6v battery, based on that, it appears you'd be able to light the strip for a 5 minutes or so.  But you'll never get 16A out of a single battery.  So it ain't going to happen.