I saw an interesting analysis by Steve Kornacki on MSNBC this past Friday. He displayed a chart listing ten battleground states Trump won in 2016 that showed which candidate is favored to win each state and by how much. Then he demonstrated what would happen if Trump lost one or more of those states this year.
I recreated his chart below with an additional column showing how many votes each state has in the Electoral College.
The chart answers the question in the title of this post: How many of these battlegrounds that Trump won in 2016 could he lose to Biden this year and still win the election? The short answer is that he could lose the three battlegrounds in which Biden is leading by the largest margins — Michigan, Wisconsin, and the Nebraska 2nd* — assuming he wins all the others. But if he were to lose those three plus just one more (except Iowa; it would need to be two more including Iowa), even if he won all the other others, he would fall short of 270. In fact, putting aside Iowa and Nebraska-2, if he loses any three of these states, he loses the election.
Note: An earlier version of the above chart had incorrect polling numbers for several of the states. It was corrected at 2:34pm on 26-Oct-2020.