There are a lot of things he could have done. Are they good? That's another topic.
** Could have done **
One thing he could have done better would have acted faster on the CDC and FDA. It wasn't as obvious initially but they were horribly and incompetently mismanaged that limited the pace at which they could respond. He resolved that fairly quickly and we have had drugs tested and moving through approval faster than has happened in fair history.
Identified at an earlier stage that the previous administration had left stockpiles of PPE virtually empty. It should have been identified very early in his administration that we did not have the stockpiles we should. He did however effectively work with the private sector to rapidly pivot and produce the items we needed such as Ford building respirators, MyPillow making high quality masks, and others to a capacity that exceeded our own needs that we could export to nations that were having challenging times.
He could have probably pushed harder against the narrative of the WHO which he likely had intelligence to some degree that they were blatantly lying to the world and taking direction of China. We now clearly know they knew this was airborne communicable while they were still publicly stating it wasn't. I would be surprised if the CIA and NSA had not known this to be the case but I'm not 100% sure what he would have done as, again, panic could have been just as dangerous to lives as the virus.
He could have perhaps identified our manufacturing deficit when it came to medication for which we are heavily dependent on other nations, namely China, for when he entered office. This put the US in a very difficult position when it came to moving quickly and as well as punishing bad actions by the CCP such as the cover up of their outbreak.
Provide and clearly define what a COVID death actually was. We have many cases up number adjustments both up and down all across the nation. Actual verifiable cases from people passing from being shot or auto accidents being counted in the tallies because they were infected though it played no role in their actual death. This would have heavily reduced the panic as the numbers would have been much lower in fatality. According to the CDC we now know the mortality rate is approximately 0.26% within the US across the entire population. This could have prevented large scale economic damage, increased suicide, drug use, homelessness, and other reactions to the governors in numerous states either malicious or ignorantly acting.
** Now an important thing to remember **
President Donald J. Trump is not a dictator. Maybe people in other countries (or even in this one) don't seem to understand that the United States is a constitutional republic in which our founding documents explicitly restrict federal powers over states. He can't easily force the states to do anything. Which is why we are at something like 130 days of riots in a certain city. He can't easily just walk in, take over, and storm the streets nor could he keep Cuomo, Whitmer, and others from putting a bunch of sick people in elderly homes which enormously inflated the death toll in the US. Some estimates have Cuomo's actions alone conservatively placing him responsible for 20,000 deaths but as many as 40,000.
** What he didn't do wrong: **
Travel ban, he did take that action against advice from people such as Dr. Fauci and in retrospect Dr. Fauci said it was the right move. This was while Joe Biden was calling him a racist xenophobe for enacting it and numerous high level democrats were encouraging large gatherings. As per a number of court cases regarding other travel restrictions President Trump, as do all presidents, have broad authorities on immigration restrictions. The criticism I am seeing largely seems to be nonsensical from the media and key democrat members. They claim he was still letting people into the country. Those people were US citizens for which we have no justification at all to legally bar from entry. We can't just willy nilly make them effectively stateless which some are suggesting we should have done. At best he could have possibly enforced a quarantine which any member of that group could have challenged in a court. Due to a number of legal structures their port of entry could have heavily impacted the outcome of that ruling well beyond the reasonable quarantine as various states have very different authorities during an emergency. Mine for instance can ban the sale of explosives, alcohol, and only legally quarantine the sick. Few other things that are inconsequential however they cannot detain or quarantine anyone that is not provably sick. Trump not only listened to all expert advice to date but experts have said that defying them likely saved thousands if not hundreds of thousands of lives. This case in particular. The travel restriction is a prime example where he was effectively the only person in the room according to witness accounts willing to make that decision.
Mask mandate? Despite what @JonathanReez said the president has no authority under which he could mandate masks. Not to mention none of the numbers he has provided would hold up to scrutiny. It would immediately face and fail any constitutional challenge at a federal level. At best it could have been maintained while being challenged in the court. Numerous forced dress standards have face court challenges at various levels from state to federal and lost. For instance woman can legally be topless in some states and we have well established no one in this country can be forced to wear religious garb. This would very easily be smacked out under a 10th amendment argument as have numerous other attempts for presidents to enforce power on states. Masks haven't even been to be clearly determined to be significantly effective based on analysis across nations.
Some claim he should have been alarmist on the issue. What happened when people were alarmed? There were runs on food, toilet paper, panics, actual violence, and all that was without him screaming bloody murder about an infection that has turned out to have a fairly low mortality rate. I think people arguing against this don't understand what life, liberty, and property damage could occur in a panicked populace. Think of Katrina or the like. We likely would have lost many lives as people are fighting over what they deem essential. Supply chains are elastic and even the gradual run up for the product runs stretched them to the point of nearly breaking. If anything he should have even been less alarmist as there are number of cursory harms that happened simply because of extreme reactions by some states.
He did NOT hold up relief bills. Nancy Pelosi and other leading democrats repeatedly were putting unrelated content in these bills when he was pushing for passing small targeted bills. There were numerous attempts by democrats to bail out localities that had been facing large budget deficits. To tie in mail in voting. Does anyone remember that during the first one they wouldn't pass it in the house without funding for the JFK Center for the Performing Arts then they immediately let a large number of their staff go. Pepperidge Farms remembers.
There are so many nonsensical uninformed replies here I could fill this section up well beyond the limit I'm sure.