I know this is now a bit old, but I was so pleased to finally beat Carrhae that I had to post...

Like Cerberusti I went for the big hill behind and to the right of where you start. I have now beaten the game multiple times using this strategy on medium.

Firstly, set you cavalry to charge the archers behind and to the left of you as you start. This is to drive the horse archers (HA) away.

Put all legions into standard formation asap. Also fire at will.

As soon as they are out of testudo, pull the center two legions back at charge speed. The idea is to turn the n formation you start with to a u that the cats will charge into. You will have just enough time to pull the units back and turn them to face the cats.

Meanwhile have you cavalry charge forwards after driving the HAs away for a short distance.

Target you cavalry to charge the flanking cat units on either side. This completely disrupts their charge. Meanwhile the two center cat units rush into your u shape - charge them from the sides and behind.

The cats will rout with heavy losses in less than 30s. Do not chase them.

Start running all units to the hill behind your starting position. If you are lucky a few HA units will charge you - turn and kill them (your cavalry is v good at this) then continue.

You will meet the enemy general on the way to the hill - overwhelm and kill him

Get to the top of the hill, put you general way back out of arrow range and put all your legions into testudo.

Wait for the HAs to run out of ammo.

You will have to come out of testudo to deal with the other enemy general charge - get back in asap.

Once the HAs start charging up the hill (out of ammo) your legions can easily defeat them. If you can spare a cavalry unit, chase routing units off the map cos otherwise they regroup and cause more hassle.

I usually have 370+ kills with this strategy and 40+ troops surviving. Keep your general alove at all costs