Trigger tuning is pretty easy on stuff like this, but keep in mind the parts quality isn't what is found on your average firearm.
If you've figured out how to take the sear out, you can remove a small amount of the part of the tip of the sear that holds the hammer back. Take out your sear return spring and look at it- Orchard Supply/Lowes/etc all carry springs, so find a lighter one and install it.
A small dab of something like Slick-50 wheel bearing grease on the sear nose will help smooth things up. You can also pretty easily put an overtravel stop on the bottom of the trigger guard to keep the trigger from flopping back once the sear "breaks". I got one from Brownells that had a neoprene insert in it so the trigger had a soft "stop" against the trigger stop.
On a Sheridan pisol I worked on I also put a take-up adjustment into the top of the trigger guard by drilling and tapping for a 6-48 screw that I could adjust. Once I was done there was very little movement required for the trigger to break, and it held up for a couple of years of heavy use.
You want to proceed with caution- accidental discharges are no joke, even with an airgun. If you don't feel confident find a tuner who does that kind of work.