You can turn on the lower transistors with 3.3 volts through 1K resistors, if the motor doesn't draw more than around 52ma! And, using NPN transistors for the upper transistors will require a much higher voltage on the bases. If you need to drive the motor with 12 volts, then the voltage at the base of each of the upper transistors will need to be at least 12V + 0.7V + whatever the saturation voltage of the lower transistor is (1.1Max at 4A).
So, there are two problems here:
1. Probably not enough drive on the base of the lower transistors. I'm assuming the motor will need more than 52ma to run, else why use 2N3055 which are intended for much higher currents (15Amps max!). The collector current is going to be the base current times the hFE (20-70 at 4Amps and 5 at 10Amps). So, if the motor requires 4Amps, then you need 4/20=200ma at the base. Since I doubt your arduino outputs can supply 200ma, you will need another stage of amplification -- i.e. another transistor -- and the base resistor on the 2N3055 will need to be (3.3V - 1.5V)/200ma=9ohms or less [why 1.5V and not 0.7V? Because, at 200ma into the base of the 2N3055, the Vbe is going to be more like 1.5V (whereas at 52ma it will be more like 0.7V)]. But, lets say your arduino can supply 20ma, then 20ma*20= 400ma. So, if your motor only needs around a half an amp, then you might get away with it (and the hFE might be higher at this lower current, so you might be able to get away with an even higher motor current, but then, you would be out of spec, so not a good idea if this is to go into production.) Or, you could use a darlington, as suggested by Mr. Valentin, in which case, 1K might be just right, but do the math.
2. The upper transistors need to be driven with a much higher voltage (look up emitter follower circuits). Again, more transistors--as you will need to apply a voltage of around 13.8 volts.
You would be much better off using PNP transistors for the upper transistors (like in the schematic supplied by Mr. Valentin).
