Qart-Hadasht (2.35A makes the Barcid reforms MUCH easier to achieve thanks to the increased likelihood of Barcid FMs)
Early game difficulty: very easy
Mid game difficulty: medium
Late game difficulty: easy
Army/unit
Carthage was famous for hiring diverse mercenaries from around the mediterranean, and EBII does that fact justice. I can't possibly write down every one, so I'll just list the notable ones
African
Numidian Noble Cavalry begin the game with 9/13 stats. Above average for skirmishers, but should you achieve the Barcid Reforms and then wait for the Renewed Panoply Reforms, both of their associated armor upgrades will increase the Numidian Noble Cavalry's stats to 9/15, making them on-par with Gallic Noble Cavalry!
Libyan Swordsmen and Late Libyan Infantry are two post-Barcid Reform units that are above-average swordsmen and spearmen, respectively. The swordsmen in fact gain an armor upgrade after the Renewed Panoply Reforms, making them a 10/21 swordsman unit - on-par with Polybian Principes! Well, except for the tomahawk missile javelin attack...
African Elephants are a smaller breed than the famed Indian Elephants, and as such should NOT be used. They are almost as expensive as the Indian variant with much lower health, meaning a much higher chance of running amok from taking damage. Only use if your playstyle maximizes the use of the elephants' terror.
Libyan Cavalry now wear armor, boosting their defense by 2 points and morale by 1 point. Now their stats are 5/10, about on-par with both variants of Celtic Light Cavalry.
Hellenistic
By investing colony points into Syrakousai and Lilybaeum, you can train all the generic Hellenistic troops. Of note are the Late Hellenistic Heavy Lancers after the Thorakitai Reforms which are one of the heaviest cavalry units you can train.
Tyrrhenian
Liguro-Corsi Slingers are a 2.35A gem. With 7/13 stats, they can plug holes in the frontlines much better than most slingers. Sardinian Warriors also have 7/13 stats, but with more defense coming from armor than shield. Thus, they are better at defending from missiles on the move than while stationary than say, Ligurian Spearmen. Both the slingers and spearmen are fine light troops.
Celtic
Gallic Swordsmen and Mercenary Gallic Swordsmen now gain armor upgrades after the Thorakitai Reforms. Rhaetic Axemen are back on the menu, and can be recruited south of the Alps using the revamped foreign military colony recruitment. They are almost identical to North Arabian Thureophoroi stat-wise.
Iberian
Lots of new and revamped Iberian units! A lot of Celtiberian units had their armor reduced by one point initially in accordance with the new Scutarii Reform armor upgrade which restores them back to their original values. The Celtiberian Riders unit, though, is different. They still have their initial 8/12 stats, which become 8/13 post-reform, making them a rather study light cavalry unit.
The Celtiberian Mercenary unit is very strong, but sadly recruitable only when the Celtiiberian capital of Sekeiza remains under their control.
Blastophoenicians are a spearmen unit with similar stats to Libyan Late Spearmen, but with a mass of 1.1! They will absorb cavalry charges admirably.
Use. Iberian. Medium. Swordsmen. They have identical total stats with Polybian Principes, but with more points in defense skill than armor. Unlike the Libyan Swordsmen, however, Iberian Medium Swordsmen pack soliferrum javelins! They can also be recruited all around the Western Mediterranean including Nurri (as settlers).
Campaign
Let's talk about the new starting situation of Carthage in 2.35A. There's a new popup scroll entitled "Fall of the Eagle" referring to Pyrrhus's failed attempt at taking Lilybaeum and later death. However good news his death was, his legacy still lives on in the form of heavily damaged buildings in Lilybaeum requiring instant attention. The Syrakusian stacks will capitalize on Lilybaeum's situation by besieging it on turn 3. The new Libyan Garrison script will sap away your Libyan unit pools periodically as well as some maintenance cost. All the while Numidia seems much more eager to betray you by camping large armies at your borders.
Carthage will rise again from the ashes of the Pyrrhic Wars though, and forge a new Barcid destiny. Achieving the Barcid reforms thus should be your primary goal. 2.35A makes it much more likely for Hanno (your starting Barcid Rab-Mahnet) to force his political views upon his children, meaning you no longer have to keep him alive to the age of 73 to achieve the Barcid Reforms ASAP.
Anyways, start by negotiating a ceasefire with the Epeirote diplomat groveling near your capital for 3500 mnai. This also bumps up your FL's authority to 5.
Begin your military moves by consolidating your forces under Hanno to wipe out the easy Syrakousian stacks and taking Syrakousai. Make sure to have your Faction Heir on standby to govern Syrakousai. His excellent traits and max influence will keep the city under control once you've enslaved it.
Next, train a unit of Lithiboloi and recall your full stack back to Africa. Train up some reinforcements as well. Your mission now is to wipe out the Numidians so that you can focus on achieving the Barcid Reforms without a thorn in your backyard. Besiege and take Capsa and Kirtan on the same turn, then make your way towards Sigan and starve the remaining Numidians out. This will activate their hording, so use your spy/spies to track down each surviving Numidian stack and family member and crush them. Numidia is destroyed once all family members are wiped out. This is where those reinforcements come into handy - you can use them to either garrison your core settlements in case the hording Numidians reach them before your main army squashed them, or use them to replenish your main army.
Now that your backyard is clean and all you have to deal with are small Numidian raids on your capital every 40 turns or so, you can focus on achieving the Barcid Reforms. Begin by orchestrating a series of political "assassinations". Every male of the Faction Heir's family tree must be sent on a boat to Krete where the natives will take care of them. For roleplaying purposes you can also "suicide" every anti-Barcid FM, though this isn't required. Once Hanno becomes FL, his family tree of Barcid cronies will forever be in the line of succession. You now have two options: either use your navy to perpetually blockade Massalia/Emporion or the Romans so that Hanno remains Rab-Mahnet for life, or squeeze in a period of peace to manipulate one of his Barcid sons into becoming Rab Mahnet. The second option should only be pursued if said sons are Charismatic and Barcid. If they rebelled politically against their father, then you must keep Hanno alive. Anyways in order to rig the elections, right before you declare war and the Rosh demands a Rab Mahnet, have all family members evacuate all settlements with a Council Administration building (Qart-Hadasht begins with one, but you can also build it in Atig, Adrumet, and Lilybaeum), save for your Barcid crony. The next turn, assuming that he is old enough and has enough wealth (station him in well developed settlements such as... Qart-Hadahst for several turns to build up wealth), he will become Rab-Mahnet. Once one of Hanno's sons becomes faction leader while Rab Mahnet you will have finally fulfilled the most annoying requirement for the Barcid Reforms.
The other requirements are easy. Fight at least 6 large land (11+ units) against roman armies. They don't have to be lead by family members, nor do yours, and it can be defending or attacking. Fight 10 battles anyways just to be safe in case you're going with the "prolong Hanno's life indefinitely" route. To do so send spies into Italy, and wherever you spot a sizable stack, send in a strike team to defeat and RELEASE them as many times as it takes to reach 6-10 battles.
You also must have taken Mastia (it'll be renamed Qart-Hadast), and held onto Gadir and your starting capital.
Once all of these requirements are met, the Barcid Reforms will activate a little after turn 140. Congratulations, you've unlocked MUCH better government options and MUCH better troops!
From here you can expand in Iberia first to save the Romans as the final boss, or knock out the Romans early to put down a sleeping beast before it awakens. In any case, once you've secured the western Mediterranean, the Epeirotes will be the post-game boss. Their king Pyrrhus's actions will forever remain a grudge point, and they must be punished.
As a side-quest you must contend with the infamous "Desert Wars" where the Ptolemies will send armies upon armies across the Libyan Desert. Have a large sum of money handy to quell them into peace once they've taking Cyrene and triggered the treaty-war script.
You should also NOT use ANY colony points to build or upgrade Phoenician Settler Colonies until you've used them to build Council Administrations in Lilybaeum, Atig, and Adrumet. Each requires a City-level settlement and Waystations and Garrisons. The reason for this is that Council Administrations each generate 1 colony point every 16 turns. Play the long game by developing those cities to City level ASAP, which means upgrading their farms, putting a good family member to govern them, and building and upgrading Temples of Tanit.
Carthaginian family members are the best by far at converting the cultures of rebellious settlements. This is thanks to the Wealth trait line. Stay in well-developed settlements for a few years and your family members can advance all the way up to Fabulously Wealthy, which grants a hefty +3 influence! Combined with all the offices that FMs can achieve, as well as the aforementioned Phoenician Settler Colony buildings, and you can Punicsize foreign lands in a matter of years!