Have Britain lose the Falklands War
A crushing military victory for the IRA is all but impossible (barring some catastrophe crippling Britain, which would have to be of a magnitude that its legacy would end up dominating your alternate London far more than that of the Troubles would), but they might be able to pressure the British government to cut its losses and withdraw from Ireland rather than go on fighting an endless guerilla war. Think Vietnam for a comparable example; the Viet Cong were never in a position to forcibly eject the US Army, but they still won the war in all the ways that matter.
Your best bet to achieve this is to have the left wing faction of the UK Labour Party gain power and negotiate a retreat. This faction was generally quite sympathetic to Irish Nationalism, but in real life they lost control of the party after Thatcher drubbed their leader Michael Foot in the 1983 election. She was able to do this despite having trailed in the polls for most of her term because in 1982 she won the Falklands War, giving her popularity a massive boost.
In your timeline, however, her decision to fight backfires (the Argentines get lucky and manage to sink the British carriers, making the long range campaign impossible) and Labour rides the backlash to win the next election on an anti-militarist platform of avoiding further loss of life in colonial conflicts. Negotiations would still be fiendishly difficult and take a long time (the IRA didn't yet recognise the legitimacy of the southern Irish government, complicating things), so the process could well last into the early 90s. Nonetheless, it's quite possible that Foot or a sympathetic successor like Tony Benn would eventually agree a deal handing over the North to Dublin. A referendum would have to be avoided as the Unionist majority would presumably still vote against such a deal, so the Troubles would be regarded afterwards (both by triumphalist Nationalists, and by angry Unionists and Tories accusing Labour of betrayal) as the IRA having unified Ireland with the armalite rather than the ballot box.