The Trail of Tears was indeed horrible, and I won't claim anything better than a mixed legacy for Jackson.
But from a purely numerical standpoint, the Trail of Tears claimed the lives of about 4,000 Cherokee, but let's bump that number up to 25,000 for the sake of argument, a drop in the bucket of evil acts perpetrated against native populations by Americans, a smaller drop compared to what Europeans as a whole have done, and a molecule of what conquerors as a whole have done. That doesn't justify it, but it does put it in perspective.
To say that there's a short list of those more terrible than Jackson goes farther than is reasonable and ignores that he was all for enfranchising the common man and rooting out corruption (although in practice neither of those worked out quite right).
That may be, but Jackson was maybe not
directly responsible for all the deaths, but was responsible for enabling white settlers at the time to settle within the coveted Cherokee, now Georgia territory, despite a prior series of treaties that placed protections on the Cherokee.
Earlier in his life, he had an adopted Native American son, whom he neglected, and would not teach him, and the boy died in his youth due to disease. Jackson concluded that all of them were animals, were dumb, and had inferior bodies. This was ill-concluded, and historians usually deduce that the actions during his military campaigns and presidency were motivated by this.
Now, naturally, his conclusions during the time were not unusual, and even Lincoln said, closely paraphrased, "I do not think that the black man should be equal to the white man." Many historians argue that this was what Lincoln believed, judged by other statements of his, even though most people tend to cast him as an idealist. Despite popular belief, his actions concerning slaves were primarily strategic.
Thr point is that despite what people say about the "badassery" of Jackson or Lincoln, they both held similar views towards the colored people of the time.
