Turning on many (30) leds arduino mega
This page explains that the ATmega2560 could drive up to 800mA: Arduino Playground: Arduino Pin Current Limitations
There are limitations for groups of pins, so you have to be careful.
The 800mA is a lot in my opinion. I wonder how hot the chip will become.

What kind of leds do you use ? Normal 20mA leds ? Or is 10mA leds also possible ? 30*20mA = 600mA, but 30*10mA is only 300mA. The 300mA seems a lot safer to me.

With Charlieplexing the leds are not 'on' all the time. However, with the Arduino Mega 2560 you have enough pins, and you could just lower the current through the leds.
Turning them on for a short time (without Charlieplexing) is the same as turning them continuous on with a lower current.

The most common way to drive 30 leds is with a led strip. For example a led strip with neopixels. That led strip has to be powered seperately.

My advice is to lower the current for the leds to 10mA and hope that the ATmega2560 doesn't get too hot.

[ADDED] 300mA is still a lot. Start with 5mA per led for a total of 150mA when they all are on at the same time. Many modern and good quality leds are bright at 5mA.