How do I know what the right signal amplifier to use is in order to program a hall-effect sensor?
I see from your previous question that you appear to be trying to do this with resistor dividers and switches; I feel that's very unlikely to work. There's a reason the official dev kit costs $500, and that is that this programming scheme is quite onerous.

Bare minimum required from the datasheet is something with rise/fall times of &lt;100us for a 5V -> 27V transition. Current isn't clear, but the largest value in the datasheet is 300ma for fuse blowing mode, so let's use that as our target.

I would build this in three phases:

1) Get a suitable power opamp, configured with a fixed gain: http://www.electronics-tutorials.ws/opamp/opamp_3.html ; if you pick R2 = 1k RF = 9k that will give you a fixed gain of 10. LM675 is a possible opamp: http://www.ti.com/product/lm675 : its supply is good up to 60V. I would use a supply a bit above 30V to make sure the amp has headroom. Obviously the power supply also needs to be suitably powerful.

(While the opamp is cheap, the power supply may not be, if you don't already have a bench PSU)

2) Generate the desired pulse train using a microcontroller DAC in the 0-3.3V range. Vlow=0.5v, Vmid=1.5v, Vhigh=2.7V.

3) TEST EVERYTHING: using a scope, check that you have the desired pulse train coming out of the DAC, with correct timings. Connect the DAC to the amplifier, and a dummy load (eg. 10k 1watt resistor) to its output. Check you get the right pulse train.

Wire up the sensor and test it for real! There doesn't seem to be any way to confirm programming, so I guess you just have to measure the output.

Note: the reason why Am I following the procedure to set the sensitivity in Try Mode for the A1362 Hall-Effect sensor correctly? didn't work for you is that you have to keep the programming supply at at least 5V at all times - pulses that go to zero abandon the programming sequence.