I had to do this for 2+ weeks with one of my hens. I found the easiest way to do it was to have the pre-measured syringes all lined up (there were 2 antibiotics and some ENSURE of all things!!!) and ready to go. Then my daughter - the resident chicken whisperer - would scoop her up and hold her calmly and gently pry open her beak with her fingernail. I would then squirt in as many syringes in succession as I could manage, angling from the side of her beak and as far in as I could go, giving the poor bird a breather after each one or two. It did get easier with time.
I can't even imagine how you'd do it all by yourself and not wind up with meds all over yourself and your bird. Hope it goes well!