Read all the above posts. Agree with most points.

I am playing hard/hard on short campaign and it is a lot of fun. Main lessons:

-you WILL be fighting a lot of factions simultaneously. At one point I fought battles with Scipii, Brutii , Julii , Numidia ,Spain and Gaul (yes, Gaul!) in a single turn! Except for the Romans, all the other factions initiated hostilites first.

-Tactical skill on the battlefield is paramount. This is not a faction where you can sit back, build up and then attack. Needless to say, you have to play out all battles personally and pull out all the tricks to keep your losses to a minimum: use missiles to take out roman infantry or enemy units in the city square, attack only when you have overwhelming force (you don't want to win a tough fight, you want to crush them in an easy fight), take your time to maneuver into position on the battlefield. You cannot afford to rush an attack and then count on production to replace your losses.

-Best carthaginian weapons you have are Round Shield Cavalry and the initial army in Sicily, which has elephants in it. Slingers are good at taking out units in city squares with minimal losses on your side. Numidian mercenaries are easy to get and useful against, who else, the Numidians!. As others mentioned, Carthaginian infantry is no match for the Romans or Greeks.

-You need a strong navy. Your holdings are on 3 islands (baleares, Sardinia, Sicily) and 2 continents (Spain and Africa), all separated by lots of water. The link is your navy. Build lots of ships and keep them together, while picking off enemy ships one by one. You can effectively defend sicily and africa from Roman attacks by sinking their ships before they land (of course, sometimes they will slip by. Then you cut off their retreat!).

-Carthage has 3 power bases: sicily, Africa, Spain. You should strive to expand 2 of them at least. In my campaign, I chose Sicily and Spain and kept Africa/Numidia till later.

Sicily. Since the Scipii are your sworn enemies, it pays to attack them quickly before they build up. I managed to blitz the Scipii out in the second turn by using the elephants to smash down the city gate. Without Sicily, theScipii are down to a single province, and they will be slowed down a good bit. If you have naval supremacy, blockade them in their capital Capua and sink all their ships, so they cannot attack you in Sicily.
If you are good tactically in fighting phalanxes, take out the Greeks too. They are too weak to reinforce/retake Syracuse and it is a well developed city. I did this in about turn 4 or 5.

North Africa. The Numidians will attack you sooner or later. Players on very hard reported they got attacked immediately. In my hard campaign, they attacked in about turn 20 (260BC ) after they ran out of places to conquer in the Sahara and Gaetulia. In any case, the good news is their units are weak. Buy Numidian mercs to counter their own cav.

Spain. You should make an early decision whether to hold on to Corduba or to abandon it. Cordoba is a rich province, and if you beat off Spain, it is pretty safe from other enemies. On the other hand, war with Spain will cost money that you need to fight other, closer, enemies.

Spain starts with 4 provinces against your single one on the peninsula. Therefore, you need to even it out by capturing one of their settlements early, before they start making their better units. Cartago Nova is the logical choice because it is closest and is on the Mediterranean, so it can link up with your other provinces. Once you take it, it becomes 3 (poor) spanish provinces versus 2 of your own on the peninsula. Much better odds!.


Other settlements:
-Lepcis magna in Lybia. It is rebel held, without a wall and defended by a couple of town militias. Easy to capture, so grab it before the Numidians get there.
-Caralis on Sardinia. The Julii will attack (usually about turn 4 or 5). I think it is best to abandon it. You just won't have enough forces to defend it and still fight in Sicily, Spain and Numidia.
-Palma on Baleares. Try to develop its population quickly: lower taxes, build Tanit shrine, etc. The aim is to tech up to port and produce ships. It is also a good source for mercenary slingers.
- Finally, a couple of warnings:
Etna will erupt sometime around 260BC. Any army you have in the close vicinity will suffer huge losses (about 40%) . So keep your main force on the Island somewhere else around that time.

The Spanish units are identical to yours, so they can bribed back and forth. I lost a 500 veteran army to bribery . It took me many turns to first, defeat it, and then replace it. Needless to say, I returned the favor later on by buying an attacking Spanish stack.

Hope the above helps.