Hmm, if you can't do this, then you probably don't have "everything" about singing locked down. In fact famous opera singers wouldn't even dare make such a claim.
The reason I say that is that there's really no secret to it. If you have problems doing this, then it's really an indication that you've got some bad habits in your technique. That's no slam on you, it's just bound to happen because we are our own worst vocal coaches.
There's no secret to how to do this really. It's just air. Relax the neck, don't raise or try to push the air out with your larynyx, do it all from your legs up. Relax your throat and make an "inside smile" - like you've bit into a hot potato. One trick that's pretty common is to practice it top-down. Sing the highest note and then keep your voice in that same placement and sing the lowest. That way, you're able to do it, your voice is already in the correct position to properly make the leap.
If you don't do this already for the big leaps, then you're catching the air in your throat and having your throat push it out, which is cheating.
It's tough to do it the right way, but your vocal chords will thank you and it'll take the grunt work off your throat.
There's no shame in taking voice lessons. Even the most famous singers take voice lessons. It's also fun!
My voice teacher always loved to pick songs for my rep that would have these horrendous leaps in them. There's one otherwise easy student aria, that she actually CHANGED to put a leap from C (above middle C) to Ab (the one above the staff on a ledger line) - and thinking back, I can't even remember the way the aria is supposed to go. Her way sounds normal, and it's a workout. You need a voice teacher that does evil stuff like that to you.
And whether or not you slur it - the technique is exactly the same, only the slur might make you put more weight on the lower note, which is wrong and makes it harder - which is why you should practice from the highest note down.