1st lesson for range.
Well the real key as always is to move the air faster and farther.
To keep abdominal reserve strength work on a natural approach below 4th space e . If you place your hand on your stomach and sing a g or c you will find that you do not tense your muscles. Check to see if you are using this same relaxed approach to playing.
It only takes a day or two to learn this and you have more strength to speed up the air in the high c area.
For the mental part there are several points. Low notes are more non-directional than high ones. All you want to do is let them roll out of the bell onto the floor. Nice and relaxed using warm breath (haaa). The higher notes are directional and you want to shoot them through the horn to the back of the room. Use cold air like cooling soup.
Music is an expressive art not an athletic event. Don’t go for records work on painting a picture.
As for the chops always set them for a g on top of the staff. This can prevent dozens of problems. Plus it is only an octave to high g over high c and an octave and a half to low c. Most problems come about because the set was on a low note like second line g. Now you have to muscle two octaves to get to g over high c. This is really a big deal. It is easier to set for the upper register and relax for the low notes than to set for the low ones and fight the high ones.
Make sure that you have a close (lips touching) embouchure then let the high notes out. To get a feel for what the lip needs to do in order to play higher try this. Put your teeth together and place a pencil between your lips. Let the eraser touch the front of the teeth. The other end (unsharpened please) will stick straight out in front. Raise and lower the end of the pencil using only the lip muscles. Raising the pencil takes lip compression (lip against lip) as do higher notes. This is also used by some as an exercise to strengthen the lips.
95% of the people that ask about endurance and range exert too much overall pressure (chops, abdominal, mouthpiece) and the notes can not escape into the horn. Relax the chops and pull the mouthpiece away from your lips as you ascend. The extra compression and force of the air column are already trying to blow the lips toward the mouthpiece. Pull away and give them some room to buzz. It may sound strange but I’ve seen it hundreds of times.