In theory, the Supreme Court (one branch: judicial) could cancel the Clean Water Act as unconstitutional. In practice, it is unlikely for it to do so at this point. That would have made more sense forty years ago when it was first being applied (the 1972 version, not the 1948 version).
Clearly the act could be repealed by Congress and the President (two branches: legislative and executive).
That being said, the Affordable Care Act also has plenty of weight on it, and as I understand it, that is an Act which is being effectively cancelled by the Executive Branch alone (possibly with the support of Congress)
This is two separate things. The Patient Protection & Affordable Care Act (PPACA; popularly known as Obamacare) had provisions in it for waiving various parts of it. So Donald Trump (or whatever president) can use the discretion allowed in the original act to remove key pieces. For example, the individual mandate is within his discretion to remove enforcement. Some believe that removing the individual mandate will in and of itself send the law into a death spiral.
In short, PPACA's interlocking nature where the individual mandate funds the subsidies given to the insurance companies in exchange for tighter regulation of approved plans makes it easier to corrupt. Without the mandate, many believe that the insured will get older and sicker. That would drive up plan costs, so fewer people will be able to afford care. The younger and healthier participants will be most likely to drop out, again making the remainder older and sicker. Keep repeating the cycle until no one remains.
Other parts of PPACA are not subject to administrative discretion. For example, increased funding for Medicaid, subsidies for the exchange-based plans, and the federal exchanges themselves would all require some budgetary action by the legislative and executive branches. Since 1975, the president hasn't had an impoundment power that he could simply arbitrarily not pay for budgeted items.
The Clean Water Act does not have a single mandate that dominates the whole law such that removing it will affect other, seemingly unrelated provisions. Trump might be able to use prosecutorial discretion to effectively cancel it, but he can't make it simply not work. He would have to actively ignore cases where the government would normally be expected to prosecute. Further, he would have to do so over the protest of the existing bureaucracy. Note that some of the act is enforced through cooperation with state regulatory personnel, who will not be subject to Trump's executive actions.
The Clean Water Act lacks the same interlocking nature. What it does have is bureaucratic inertia and a long history of jurisprudence. It can't be pushed away with a single action. It might be nullified by sustained action.
Note that all this assumes that Trump even wants to nullify the Clean Water Act. It would seem more likely that he simply wants to remove some of the more expensive regulations. At least that's what his rhetoric claims. While still frustrating to proponents, that's not the same existential threat as actually repealing it.
