I am a retired electrical and electronics engineer.
You are dealing with some serious current here!
For turning on a motor use several high Power FETs in parallel. These should work from a single Arduino output of 5 volts.
The FETs should be put in the low side of the motor (to ground) and be of the N channel type
If you look on 'Rapid Electronics' or RS Components you will see several suitable FETs.
a) low 'ON' resistance. This will reduce the heat dissapated when the FETS are ON. Thus reduce the size of the heatsink.
b) high current at low gate voltages.
c) High max current capability
You can wire them in parallel to reduce the current through each device. They won't current share perfectly but heating effects will make them current share effectively enough.
The IRF540NPbF (914-8154) RS Components ( data sheet from the website) will do the job but you will need four or five of them in parallel, five to be safe, especially if you can only drive the gate with 5volts. An alternative is the IRLZ34NPBF RS 541-1247) at 77p each (a bargain).
A limiting factor is the safe operating area (graph) when switching. at 100amps five devices at 24V, then the FET must remain below the curve for 10mS using 10Amps and 12V for each device when half off otherwise PHUT! This could be a problem for continuous rapid switching.
Each FET must have its own gate resistor and although the gate current is only microamps the gate resistor should be kept low to discharge the gate capacitance when switching. Also a sudden application of power on the motor could turn on the FET if the gate resistor is too high (again due to the gate capacitance). A 1Kohm resistor in each gate should be fine, 500ohm for faster switching.
Tie all of the source pins to gound and connect all of the drain pins to the motor. Tie all of the free ends of the 1K resistors to the output pin of the arduino.
Connect both the ground of the Arduino and the ground of the motor supply (in your case the 24volt battery) together.
And remember 100Amps (peak) is going to need 16mm squared tri-rated equipment wire.
Last but not least place a hefty zener diode of greater than 24V across the FETs from drain to source as the internal zener diodes of the FETs are not man enough to take the back EMF of the motor.
There are other FETS that will do the job but at the moment I don't have the time to look. To get away with high current and high drain-source voltage usually means that you need more than 5 volts to drive the gate.
Each FET is going to dissipate 18 watts in the fully on condition (100 amps) so some serious heatsinking will be required (I could help with the calculations if required).
Get in touch if you need any more help.