This branding gives him a massive advantage in public recognition, but it has also helped him in his battles with his fellow Republican presidential candidates. So far, two main attacks have been used against him. One of them seems to have failed, and the other has uncertain prospects.
The first attack--popular among anti-Trump Twitterati--is personal: using either the politics of shame against him or outright picking a personality-oriented fight with him. Both of these lines of attack have not borne much fruit because they reinforce Trump's brand. When people attack Trump for being out of line, that's like attacking Gucci for being too expensive: the overreach is part of the brand.
Head-to-head personality battles have also so far proven a fraught enterprise for many of his opponents. That's in part because his rivals have tried to create politician brands rather than media personality brands: Ted Cruz is the True Believer, Marco Rubio is the Next Gen Reformer, Jeb Bush is the Experienced and Earnest Wonk, and so forth. To call them "politician brands" is not an insult (presidents are, after all, politicians), but this difference in branding genus has implications for how they can attack Trump. In a battle of personal nastiness, Trump can win without damaging his brand; folks with standard politician brands usually can't (Christie might be an exception to this). We expect a kind of restraint from politicians that we don't demand from media personalities. Thus, when candidates get into a head-to-head personal match-up, Trump can go places that they really can't. And so Trump wins exchange after exchange. There's a reason why Marco Rubio has avoided getting into a direct personal battle with Trump: it would very likely injure his own brand.
Campaign surrogates or independent journalists/activists have also had limited success when attacking Trump personally. These personal attacks only feed into Trump's brand as a polarizer. Moreover, these attacks keep him in the news cycle as someone important. So far at least, the oxygen given to Trump's campaign by personal attacks has helped him far more than these attacks have damaged his brand.
The second strategy is to argue that the Trump Brand is not a conservative one. In many years, this might be effective. But, this cycle, many Republican primary voters are (rightly or wrongly) so suspicious of conventional politics that they fear that, even if they vote for a "conservative" candidate, they will not get conservative outcomes. Republicans have had such great support for outsider candidates during this presidential cycle because many of them fear that conventional politics no longer constitutes an effective vehicle for realizing their policy preferences. Voters feel that they know the Trump Brand--he fights!--and thus they might think that they know what they're getting with Trump. I'm not here arguing that these perceptions are necessarily true, but they do seem to exist.
Moreover, conservatism is having a rather large debate within itself about what exactly "conservatism" means in response to current problems. Can conservatism make peace with populism? How compatible is it with the vision of open borders? What should be the national-security and foreign-policy goals of conservatives? What is the role of reform for conservatism? The proliferation of these questions makes it harder to police the bounds of conservatism. (These questions may also help prompt a re-energized conservatism, too.)
Having a well-known brand isn't everything, of course. Perhaps Trump will prove more effective at filling arenas than at actually winning caucuses and primaries. Voters may tire of the Trump Brand or may view it as ultimately incompatible with the presidency. It's also possible that attacks on Trump's conservatism will cause Republican voters to turn against him. However, at the moment, these attacks have not toppled Trump.
Looking at the failures of other Republicans to take down Trump, David Frum has suggested that other candidates might do more to hammer home policy alternatives that address the concerns of Trump's supporters:
Or maybe it’s time for the party’s elites to let go of some of their cherished inward-facing policy priorities...Instead, they might try actually addressing the fears and anxieties of the American middle class: jobs, wages, retirement security. Negative advertising has been aired without success. Perhaps a positive program would do better? Before it’s too late?Even many critics of Trump--such as Yuval Levin--have noted his skill in diagnosing the anxieties of many Americans. There's an opportunity here for candidates who clearly address these anxieties and explain directly how their policies will respond to them. Policy nostalgia or vague invocations of conservative stalwarts might not be enough to win the primary or the general election.