Looking for guidance. The 2nd part has a lip slur from Eb above the staff to Ab . Does anyone have any suggestions to improve accuracy. Sometimes I get it sometimes I don't.

All help is appreciated!

It's not a lip slur; it's just legato. Perfectly acceptable to use legato tongue on that. Make sure you don't stop the air on the way up. What helps me is to think of emphasizing the lower note - this keeps the air flowing. Try playing it on the mouthpiece alone (with no tongue), then on the horn (with or without tongue).

Thanks will give that a try.

Brad is right that you can legato tongue that and it's just fine. And if you use the tongue well, it will sound like a lip slur anyway.

As for the trip up to the A-flat, my mental approach is the opposite of Brad's. While I'm on the E-flat preparing to go up to the A-flat, I "think down" on the A-flat, like I'm coming down to it and not going up to it. For me, that centers the A-flat and makes it much easier without blipping that F# between them.

But honestly, you should just practice lip slurring arpeggios in that octave every single day. Because doing that Eb to Ab slur (and E to A, and F to Bb) happens a LOT in trombone life, and you need to be able to do it. With practice you can become adept at leaping right over that pesky F#. It just takes repetition.

I take to heart something that is drilled into student pilots, which is, "There is no substitute for flight time." Same with trombones.

But legato tongue and thinking "down" on the higher note works for me.

Hard to give specific advice without seeing you, but one thing that many don't do enough is using the tongue level/arch within the oral cavity when going up to the higher partials to speed up the air. I find it especially critical for that particular partial because it tends to be less stable than the surrounding partials, on many if not most horns. The airspeed needs to be really just right.