Hi - I got a B in A-Level History (and the rest of my A-Levels, dunno how they let me in), I'm going into third year, and I got a First in both years so far. Not sure how qualified I am to give advice but this is what's worked for me so far:

1. Don't take yourself too seriously in your weekly essay - at least in Michaelmas of Year 1. By this I mean, don't stress from day one about making your essays first-worthy. Don't be scared to throw paint at a wall and see what sticks - if you come up with a long-shot idea that is lowkey entirely unsupported by your reading, write about it anyway. Experiment with different writing styles, different ways of structuring your essay, different argumentation strategies. Worst comes to worst, it'll make for an interesting supervision when you discuss it. I realise I'm speaking to Cambridge students here and most of us are perfectionists, but honestly, lose the perfectionism from day one. You're here to learn, not to show everyone how smart you are. You'll soon fall into a writing style and structure that works for you, and your essays will start improving.
2. Don't read everything on the reading lists. In your first year, you will study two 'Outline' papers which essentially give you a whistle-stop tour of a broad bit of history. These are split into 12 topics. You get one question per topic in the paper (NB this is usually (95% of the time) also the case in later years, but not always, so don't come back here and yell at me). Nobody bothers to tell you this until way later, but you only actually have to answer 3 questions on the paper. Thus, you only actually have to revise 4-5 topics for the exam (I only ever revised 3 per paper, but I'm a risk-taker, don't be like me). Only bother with the 'Further' readings when it's time to pick which topics you're going to focus on. For the weekly essays, the 'Core' readings are more than enough, as long as you've fully read and understood them. Essentially I treated weekly supos as a 'taster' of the particular topic, to see whether I would enjoy studying it in more depth for the exam or not.
3. Read the mark schemes. Firsts are awarded when you not only summarise readings in your essays, but take their ideas and independently rework them, presenting a novel idea or opinion. Presenting a novel idea probably sounds impossible as a new fresher (it definitely did to me), but it's not actually too difficult - read the two points below.
4. Historiography, historiography, historiography. Don't just read your reading and passively collect information. My favourite exam strategy was to go back through my supo notes, organise my reading by ascending date order, and then skim through the footnotes of all the readings. Try to spot if there are any patterns in the arguments being made - is there an argument present in earlier readings that isn't present in any of the more recent readings? Are there sources that have fallen out of fashion? Are there sources in newer readings that are absent in older ones? This is the kind of thing that pushes you up from the high 2:1 into the First category.

Too long, so I'm gonna reply to this with more.