My 2009 Hyundai i30 is having trouble starting

A car that is difficult to start could be suffering from, literally, hundreds of different problems. You need to have the car electronically scanned to see if the on-board computer has logged any faults of glitches in the fuel or ignition system. That's the best way forward or you could find yourself replacing perfectly good components without any change in the car's behaviour.

And don't rule out basic stuff like a battery that seems fine but is struggling to turn the engine over as well as supply enough power for the ignition to work properly. Modern cars with electronically controlled major functions really don't like a battery that is slack and cold weather will often show that problem up.

Also, when you say you've checked the fuel filter, what do you mean? Did you replace it or simply do a visual inspection. You can't really tell by looking at a filter how gunked up it is inside, so while it all looks okay, it could still be a contributing factor in your starting problems. An accurate diagnosis will also be easier if the mechanic has more information to work with. So start taking notice of exactly what is happening. For instance, is the car more difficult to start hot or cold? Does leaving it overnight make a difference to trying to start it for the second time that day? Does the ambient temperature have an effect on starting difficulty? Are there any specific noises the engine makes when it becomes recalcitrant? Keep a diary of this stuff... it might save you money.