12 cities in 20 turns?!?
Weak!!!
With Berserks, you should be able to do much, much more.
The thing to do isn't to 100% your Science. That leaves you with advanced unit tech but little to implement them with.
A variation of the Warrior-Swordsman mass upgrade strat is the Archer-Berserk mass upgrade strat, and I can tell you the results are much, much more rewarding. You should almost never send your Berserks on overland campaigns if you can help it. It hurts them. They're sailors, not landlubbers.
The fastest I've ever conquered a civ with Berserks is one turn. Yep. One turn, no railroads, no artillery. 2 Galleys worth of Berserks per city, all cities on the coast. Not the AI's fault, the civ was Byzantine, so it was to their advantage to build coastal cities preferentially. On land, a force of 2 SOD consisting of Knights, Crusaders, Berserks, Pikes, and Catapults. Conquered all but one city with the Berserks, took out the last city with Knights. Poor Catapults and Crusaders felt underused.
Of course, with such a massive military and a GA going on, it was only natural that I keep attacking. The Incans, with their UU obsolete and GA way past were a natural target. Waited for Galleons, though. Using Galleons, you can actually attack from one coastal city directly to another nearby coastal city (with Seafaring + Great Lighthouse) and virtually never expose your Berserks to attack. Land Based Force meets up en route to the capital in a classic Hammer and Anvil move. Beauty itself.
Berserks are the only reason I play Scandanavia.