I'm not sure this will work as designed - it'll be very LED dependent.
I'd recommend a couple of things:
1. Use a MOSFET instead of a BJT.
Edit: tweaked this section due to the TIP-120's higher Vce(sat).
Switch your BJT out for an N-channel MOSFET. BJTs have a saturation voltage across the collector and emitter, and it varies with current. The TIP-120's Vce(sat) is too high for your design.
Even with a regular NPN transistor with a lower Vce(sat), you'll lose something like 0.4V in the BJT, which will translate into waste heat and might kill your voltage margin.
If this is what you want:
(12 - (3.8 * 3)) / 33 = 18mA
Consider what happens when you factor in a BJT's Vce(sat):
(12 - 0.4 - (3.8 * 3)) / 33 = 6mA
The transistor's Vce just killed your brightness!
Here's a MOSFET that would work the same way as your BJT (except that you won't need that series resistor on the gate):
http://www.digikey.com/product-detail/en/IRLML2060TRPBF/IRLML2060TRPBFCT-ND
You can also get MOSFET arrays that might be a good choice if you want to run a lot on one board.
2. Run at a higher voltage or use 2 LEDs/string.
Can you run from a higher voltage than 12V, or maybe put more LEDs in parallel?
Most LEDs have some variance in the forward voltage. Each LED might be nominally 3.8V, but the forward voltage might be more like 3.6V on some and 4V on others. If you're operating close to the rail, you won't have very consistent brightness from string to string.
On your 3-LED strings:
(12 - (3.6 * 3)) / 33 = 36mA
(12 - (3.8 * 3)) / 33 = 18mA
(12 - (4.0 * 3)) / 33 = 0mA (too much forward voltage).
If you make them all 2-LED strings instead, you'd get:
(12 - (3.6 * 3)) / 220 = 22mA
(12 - (3.8 * 3)) / 220 = 20mA
(12 - (4.0 * 3)) / 220 = 18mA
3. If you can afford it, use an LED driver instead.
You can buy off-the-shelf chips that will take care of limiting the current for you, which means you don't need a ton of resistors and MOSFETs everywhere (plus, you get more consistent brightness).
Check this part out:
http://www.digikey.com/product-detail/en/A6263KLJTR-T/620-1492-1-ND/