Implementing FIR Bandpass Filter for 1-3Hz range

there's not much penalty for using a high sample frequency.

There is an enormous penalty for high sample rate on a 16 MHz Arduino. As pointed out above, that leaves little time for computing the filter, especially something on the order of 100 taps.

100 FP multiplications alone takes around 1 ms, which means a sample rate of 1 kHz max even if the ADC sampling completely overlaps the filter calculations.