Several things come to mind from Trump's mishandling of the Coronavirus crisis which he exacerbated through his incompetence.
A good president is, at the least, mentally and intellectually competent (having high intelligence goes along with that). He or she doesn't need to be Einstein, they don't have to be egg-headish, but they do need to have some monumental intellectual powers, an ability for grasping and solving complex problems and a more than superficial understanding for policy. Bill Clinton, JFK, and Obama were all highly competent in this area. Low intelligence leaders like Trump, Reagan and GWBush whose backgrounds were either fickle or ready-made handed to them are the epitome of presidential incompetence. They run a very simple-minded approach to foreign policy and serious domestic problems...they lack vision and imaginative sweep for the modern forces at work..they just kind of react to events. As events have revealed, these aren't guys you want in charge when Crisis hits.
A good president is, at the least, somebody who stays informed about matters which affect the public health. With Trump, the February 9th study informed that COVID-19 carried a rapid transmission rate and that asymptomatic patients are "super-spreaders." Trump failed to warn the American public about the degree of risk, he failed in his duty to keep himself informed about COVID-19 and he misled the public into believing that the risk of infection was very low. Now the USA leads the world in number of infections, and Trump is on his way to bankrupting the economy just like he bankrupted his businesses several times. George W. Bush claimed that Saddam Hussein had WMDs and was in cahoots with Al Qaeda...of course that was all a lie. Basically, he lied to get the USA into a stupid occupation of Iraq which ultimately opened the door for both ISIS and Iran.
A good president shows a combination of energy and political savvy during a crisis. In contrast, Trump's combination of low energy do-nothing but keyboard warrior on Twitter is but the exact opposite. For example, Trump has been inept in cleaning up his mess -- was still shrugging the whole thing off by late February and leaving it to his VP....basically did nothing for two months to strengthen our infrastructure and showed excessive hesitancy in utilizing the defense production act...in contrast, FDR who was a fusion of high energy and a political virtuoso had mass production in the Country moving right away when he took over during the great depression and later the War after Pearl Harbor. Right now, America's infrastructure for handling pandemics is inferior to the infrastructure in countries that trump reportedly calls "Third World".
A good president shows strength when it comes time to take off the velvet glove and drop the iron-fist. Trump failed to do that in his weakness for shutting down the borders at the beginning of this thing. Although he claims that he shut down travel from China, flights were coming in and going out regularly to Hong Kong and mainland China. If he had kept himself informed, he would have understood how this thing could spread and taken drastic measures in the beginning so it didn't get out of control. Perhaps it was his vulnerability for the "great economy" that did not want to tamper with, but a good president would play for the long-run on that. Trump also failed to do that in his delay for activating the defense production act and not declaring Martial Law early on in high risk areas where 50 percent of the residents were not following the social distancing guidelines.
A good president shows steadiness during a crisis. Trump has been excessively erratic and keeps changing course for reasons that lack any merit. Trump first downplayed the coronavirus crisis. Then, he started to take it more seriously. Then he broke from the experts and idiotically started calling for the economy to start moving again the day after Easter. Now he's backpedaled on that once again and wants to extend social distancing to April 30th. That's good but all of this wishy-washy back and forth delays action. Although flexibility is good when newly discovered evidence renders a course of action idiotic, the data on COVID-19 has never changed and has always been out there for Trupm to inform himself with...he had a duty to know about COVID-19's rapid transmission rate back on February 9th when the landmark study was published. Trump's erraticism and about-faces are due to a misplaced effort on his part to prioritize the economy over public health.
That leads into the last point. A good president prioritizes public health over economic prosperity. If another country invades the USA or a virus like COVID-19 invades the USA, defeating those enemies must take precedent over running a strong economy, in the event one of those has to be expendable. If you can do both at the same time, great, but if not, economic prosperity has to be put on the backburner until the situation is under control.