Wild AC to DC for Arduino and high power leds
It looks like you are reviving an old 50cc, trying to work around the  front light and flashing relay that end up failing forever... 
Yes, a bridge 10-30A rectifier, and a overhauled boost converter is the clean solution, but consider input voltages beyond 60V (90V is not rare).Even so, in idle the rotor rpm is low, may float the lights, even leds, even arduino...
The dirty solution is to add a Little (1Ah) 6 or 12V Battery in the bike, charge it with one diode from one pole of alternator in series with a relay ( arduino will control the charge) beeing N.C. of relay connected directly  to batery, and N.O. connected to battery via 1,8 Ohm wire resistor ( charging low in high rpm). Alternatively, charge directly via 10A triac, controlled by arduino, taking care on trigger angle, or you end up having to install a stronger battery.
Shall you master your arduino, you can even control the second pole of alternator to drive the correct ~voltage to the 10W LED via another triac and series resistor (some 10 Ohm to not let the Led face to face with alternator\triac bursts).This frees you to control the four 3W Leds the normal way (common NPN transistors, open collector in series with each 3W Led, four arduino pins, one for each transistor base, via 2-10K resistors). Make this circuit breath, cause it's hot!!!