Is a euglena a plant-like or animal-like protist?
Really neither, but if you need an answer you can pick either.
The cell Euglena has been a plague to scientists, due to it not being easily recognized as either plant or animal. Scientists were so baffled, that they created a whole other kingdom, Protist, just to deal with them. The confusion around Euglena lies in the fact that it behaves like a plant in the sunlight, but in the dark behaves like an animal.
Euglena has chloroplasts that allows it to photosynthesize, and a primitive eye-spot which detects light in order for the cell to shift it's position to maximize its photosynthesis. Euglena does lack a cell wall, a defining feature of plant cells, instead having a pellicle made of protein bands to protect itself.
When Euglena goes into the darkness, however, it becomes distinctly animal-like. Instead of getting its energy via photosynthesis, in the darkness Euglena cells will grab its food, spurt acid onto it and slurp it up-- the process is same as holozoic nutrition. What's more, Euglena cells have flagellum, tails on cells which allow the cells to move and are characteristics of animal cells. It also has a contractie vacuole like amoeba, another holozoic protist.
On top of this bizarre contrast of features, recent discoveries in the bacterium and cell gene pool have found that Euglena cells got the ability to photosynthesize by bonding with green algae way back in the past, giving it yet another link to plants. So which is it? Plant or Animal? That my friend, is up to you to decide.
I hope I helped!