It looks to me like 28 groups of 23 leds connected in parallel. Except for the missing leds where they have been replaced by the rgb strip.
I'm sorry, but this is all wrong.
Leds need series resistors to limit the current flowing through them. You have none that I can see. When leds are connected in parallel, there should be a series resistor for each led, otherwise the led in the group with the lowest forward voltage will be the first to fail. Then, the others in the group will fall like dominoes. So if you want to do it like this, you would need to have soldered in 644 series resistors.
If you had used, say, 220R series resistors, each group of 28 leds would require around 320mA. That's around 9A in total. Without the series resistors, it would, until it started to fail, it would need even more current. Is your "mobile charger" power supply able to supply 9A+? If not, that might explain the dimness. Is the power supply getting hot? Are the ULN chips getting hot? I expect they are.
What I would suggest you re-wire each group of 23 leds like this:
Re-connect the leds in series (not in parallel as you have them now) into sub-groups of 5, each with a 100R series resistor. If there is a final group of less than 5, you will need to use a higher value series resistor with that group. For example, a sub-group of 3 will need a 300R series resistor.
This way, each group of 23 leds will consist of 4 or 5 sub-groups of up to 5 leds. Each sub-group will draw around 20mA, but will need a 12V supply. So your 12V supply will need to supply only around 3A. You can run the Nano's on 12V also because they have on-board regulators (use the Vin pin).
Unfortunately, The RGB strip still needs 5V. With around 50 RGB leds on the strip, this will require around another 3A. To avoid having a second power supply, you could use a DC-DC converter, rated for at least 3A output. This can be powered by the 12V supply but will need another 1.5A. So increase your 12V power supply to around 4.5A and that should do it.