Cannot look at the output current and apply that to the battery. You have to look at the output power and then figure battery current with the battery's fixed voltage. (Like many aspects of physics, only power is transferred.)
So a 30 Watt output from a battery approaching the limit of it's charge would have 3.2 Volts. Since P=VI and I=P/V, it seems that 10 Amps is enough, but the DNA has, at best, 93% efficiency so when that is factored in, we are above 10 Amps. If we put a reasonable safety factor of 1.2 in to account for manufacturing variances and to prolong battery life expectancy the figure is just a shade higher than 12 Amps.
So any battery capable of outputting over 12 Amps is going to work well and have a good long life. Anything less and it will likely be disappointing.