There's actually a fairly good chance Johnson will try to NOT get Brexit done.
As in, he won't allow his treaty to be ratified. Why? Then he won't be the one putting a border down the Irish Sea.
Instead, I expect him to try to do either of these two things:
Scenario 1
If he actually wants to get out of the EU, he'll try to get the EU to kick the UK out, so not only would he get his coveted No Deal Brexit, he would blame any issues that No Deal will definitely cause on the EU. Any lack of trade agreement progress would then also be blamed on the EU. He won't want a quick EU trade agreement anyway, because it would get in the way with his US trade agreement. He'll first want to ensure there's an agreement with the USA before even considering new trade relations with the EU. Which won't be forthcoming any time soon. This scenario is likely to backfire eventually as people get tired of more and more Brexit related bullshit. However, for many it will just be more evidence of Brussel's perceived hostility towards the UK and setting the UK up to fail.
Scenario 2
From his record, all he ever cared for was power over the UK and for that he had to consolidate the right end of the spectrum and destroy the Brexit Party/UKIP and any Tories with sense getting in the way. Promising he was the Brexit-Messiah was his means to get there. Yet, he may not actually want to be seen as responsible for the destruction of the UK's economy or the selling out of British public, industry and services to the US. In that case he might just try to keep the status quo going, until he'll find a good enough excuse to revoke Article 50. I would suspect his argument would be that the UK was being screwed over with unfair trade deal offers and strongarmed into remaining in the EU by the EU. So basically he was thwarted by bullies from getting a good deal and thereby forced to stay in the EU as a vassal state, but no worries, because with the Tories in charge they'd fight the good fight against The Brie-Kraut Continent. He'll wager the electorate will have forgotten his promise five years later, while he and the tabloids will keep blaming the EU for anything negative happening to the country in the meantime (in particular the NHS), the "theft" of industry that leaves for the mainland (thus for increased unemployment), higher taxes (stating it all goes to Spain and such), and portray it as a way of the EU trying to get back at the UK's citizens for attempting to leave.
By the way, perfect way for Russia to position themselves as the "Real Friend of the UK" too. Either way, I expect Russia will try to use the UK to circumvent its own embargoes soon enough. Plenty of Tories receiving Russian money apparently. Will we ever see that damning report Johnson's government refused to release?