What microcontroller has 20 or more ADC pins?
Many PIC microcontrollers have a lot of ADC inputs.

PIC18F45K50 with 25 analog inputs

Here you can find other PIC microcontrollers:

All 8-bit PIC microcontrollers parametric table

You can sort this by "Total of A/D channels".

However you should know, that all these inputs are multiplexed. These microcontrollers have 2 or 3 converters connected with multiplexers, so your sampling rate will be at least 8x slower than ADC sampling rate.

Alternatively you can use multiple ATmega8 microcontrollers and sync them somehow.

If you need high sample rate - you can use some 16-bit dsPIC, some of them have more advanced ADC (500ksps in 12 bit mode, 1.1 Msps in 10-bit mode).