When playing a Runner who can reliably and easily out econ you the best way to win is to have a game plan that can ignore their econ.
This is probably best done out of Weyland in core. Splash some yellow tagging cards and Snare! and wait to blow their house up.
You can also try to do this with a Jinteki deck, but it will be much harder as core Jinteki does not have the econ to support this play style.
With just core this is a little harder to do, as you do not have enough 3/2 agendas. Probably best done out of HP using Biotic Labor with some San Sans splashed in.
This should be your go to strategy for most games with core only. The Runner has inevitability, you need to win before they get there. With just the core set the Runner will have a hard time finding the cards they need. Shaper has no in-faction tutor in core, so will have to either just draw a ton or spend influence on special order (and still draw a ton to find MO). Take advantage of this, win before she has set up. Try to take a few more risks early game, scoring behind a single piece of ice when she does not have the correct breaker to go through it.
This strategy can be hard to pull off. It involves knowing your opponent and being able to bluff. However, it can be devastating. Pretending a Junebug is an agenda can win you the game. Or landing an Aggressive Secretary can blow up their rig, buying you time to score out before they can reassemble it.
This is harder to do in core, but worth a try if you are feeling adventurous. The general idea here is to play mostly economy assets and upgrades. Spam them out, making many remote servers. The runner will have to waste valuable time and money to check and trash each of your servers. Mix in a few traps and after hitting one she may be more hesitant to check your remotes in the future, allowing you to "sneak" an agenda out with no protection. With core only, this is probably best done out of HB with some traps and San Sans splashed in.
Use Defensive Upgrades/Buy Some Data Packs
You can use upgrades to protect your Agendas. In core you are limited to Red Herrings, which adds a nice tax but is not great if the runner has tons of money. If you want to play this way it may be best to invest a little more into the game and pick up some data packs. Specifically Double Time for Caprice Nisei and RP or What Lies Ahead for Ash.
These are defensive upgrades that help you ignore a rich runner. Caprice brings server access down to a weighted coin flip in your favor. Ash relies on a trace to force the Runner to try again. It is not the perfect solution to your problem but can help you get agendas out early before the runner is fully set up. Replicating Perfection (RP) is a Jinteki identity that helps you tax the runners clicks as well as money.
I also highly recommend you switch sides a few times. Playing as the Runner will give you a huge insight into how they play the game. What they are worried about, what they are looking for, when they feel safe. It will help you learn to exploit those weakness when you play Corp.