I have an Aqualisa Quartz A2 Pumped electric shower. This is the model with the long grey case. There are four ‘O’ Rings that will perish over time, causing dripping leaks, in which case they will need to be replaced.
I used O-rings that were around 3mm thick, with an inside diameter of around 22mm. You probably have +/- 0.5mm leeway on thickness, and maybe 1-2mm on diameter. Use the old O-rings as a guide, but bear in mind they’ll have compressed and hardened or perished. The new O-rings should stretch a little when positioning them.
Make sure the mains electricity and the water supplies are isolated before beginning.

The first three are easy. The hot/cold inlets and the outlet each have a plastic finger-screw nut holding each short brass pipe (called a spigot) in place. All you need to do is unscrew these, remove the brass pipes, pull out the old O-ring, fit a new O-ring over the wide end of the pipe before repositioning, and then tightening the plastic nut again.
The fittings are designed to compress the O-rings into place as you tighten the holding nut. It’s worth cleaning the brass pipe with some wire wool or a scourer while it’s removed, since a smooth surface will give a better seal.
The fourth O-ring is inside the case, and sits between the pump assembly and the mixer-valve assembly (I’ve seen this referred to as the ‘cartridge’).

You need to remove three screws to get these assemblies apart. Two are on the clamp that holds the pump in place, the third is on the left-hand side of the mixer-valve assembly. The screws are marked with the yellow arrows on the image above. So loosen the screws on the pump clamp and lift the clamp out (with the screws still in, this helps avoid them dropping into the case.
Then loosen the screw at the far side of the mixer-valve assembly, and lift the pump motor. You’ll see the assemblies separate, it may take a little wiggling because the inlets/outlets need to also come loose.
You’ll see that there’s an O-ring that sits at the junction between these two assemblies. Remove the old O-ring, and clean the joints with a cloth and/or an old toothbrush. Fit the new O-ring to the pump-assembly and gently twist the pump-assembly back into the mixer-valve assembly.

It’s normal to have to push and twist the assemblies to get them back together, since the new O-ring has to squash in a little, but they should go together without too much force. There should be no more than around 0.5mm gap left between them when everything has been re-seated. If there’s a gap of a couple of millimetres or so, then the O-ring has not seated properly. Re-do by pulling them apart, repositioning the O-ring and trying again, though it’s possible that your chosen O-ring is too thick, so try a thinner one or a smaller one so that it stretches thinner.

When they are both snugly together and seated in the case, then re-attach the pump clamp and the screw on the mixer-valve assembly.
The pump clamp should fit snugly to the pump. Wiggle the motor to ensure it’s properly seated, and support the motor while re-screwing. This is because the joint between assemblies should be lined up properly.
I’m hoping to add photos to this, to show details for replacing the internal O-ring in particular.
A few notes
Before re-attaching the case lid, make sure all wires are out of the way. I accidentally squashed the black temperature sensor wires between the bottom and top cases. They seem to have survived okay, but it was careless of me. I should have checked properly before fixing the cover in place.
The motor brushes create a lot of carbon dust. It takes some scrubbing to get it off, so latex gloves will help protect your skin and keep some kitchen roll close to hand to wipe things down.
While the motor assembly is out, I used the opportunity to oil the spindles. I just used 3 in 1 bike oil, I don’t know how optimal this is, but I’ve seen a heating engineer use similar on a kerosene pump in my boiler, and it worked really well to reduce noise.