With that team, you'll have a hard time. Fortunately, the game just provides you with the means to beat Elesa right before you battle her. All you have to do is travel south into the desert. There, you have a couple really strong ground types to choose from, Trapinch and Sandile. Elesa's team can barely touch ground types at all
Of course you have to evolve them first but that's not really a problem in bw2. I would suggest getting one, if not, both of them. If you only want one, I would go with Trapinch because it resists Zebstrika's flame charge and has a useful ability in levitate, which comes in handy against the next gym. However, the Sandile line is not too bad itself so just take whichever you want
If you insist on only using those four psychic types, then your only option is overlevellining. Swoobat and Sigilyph don't have a good matchup and along with Espeon, those three have complete garbage level up learnest. You only get good flying stab by level up and you need to overlevel to get a half decent psycic stab. Only Duosion has a good psychic stab around that level but having to fight three mons on its own will be a challenge
There is one last option if you insist on only using psychic types, Baltoy. Go to relic castle and find Volcarona. In its room are Baltoys. Catch one of them and you'll have the ground type you need. However, you'll have to evolve it into Claydol first as its stats is just horsecrap. Even as a Baltoy, it has a very good level up learnest. Ancient power at level twenty one and extrasensory at twenty eight. Since you don't want it to remain a Baltoy, wait until level thirty seven before evolving so that it learns earth power. Just be careful with Zebstrika as I believe the thing has pursuit
Having said all this, Trapinch and Sandile are still your best bet but if you insist on a psychic run, go get a Baltoy. It's probably the only way unless you want to be like ten levels higher over Elsa
