As with many guerrilla movements the idea was not to achieve a decisive tactical victory over the British forces- it was to destabilise the Northern government in Stormont to make them look ineffective in the public opinion and to cost the British enough in human lives, political and financial capital that support for continued confrontation collapsed and a favorable resolution sought.

The violence right on Britain's doorstep was a tool to fulfill their goals- not a hindrance to them as you might think. In fact they often sought to strike deeper into the UK as we see with the Manchester and Kings Cross bombings.

Their longterm objective was simply for Ireland to be united and independent from the British government with a focus on Irish nationalism and isolation of the Protestant minority.

Their strategy went through a few phases and was heavily influenced by anti colonial movements in Africa and Aden where a relatively small number of British casualties were enough to tip the balance.

The IRA believed that if they could make the Troubles economically, militarily and politically costly enough that the British would cut their losses and leave. Attacks in England were particularly effective as they got more media coverage and were intended to demoralise the British public.

In practice the British were able to counter this strategy. Using Northern Irish police instead of British troops ("ulsterisation") kept the conflict isolated while portraying the IRA as criminal rather than political reduced British public support for withdrawal.

Sources

Peter Taylor, Provos and Brits

MLR Smith, Fighting for Ireland

Richard English, Armed Struggle

Like most, if not all Irish Nationalist/Republican groups, their long term goal would be a united, independent Ireland. Some groups wanted slightly different things, such as a socialist state, or had more immediate lesser aims.

I'm assuming by the phrasing of your question that you are referring to the IRA of the troubles, and not one of the tens of IRAs that have used that name, for example the IRA, which was the army of the first Dáil Eireann.

Considering that that institution managed to win* the Irish War of Independence, partially (perhaps even mainly) using "violent methods" including guerrilla warfare in the form of 'flying columns', it is not quite so crazy to suggest that later groups, calling themselves the IRA would believe that they too could win.

It is important to note that Republicans/Nationalists/Catholics (these terms don't overlap completely) managed to achieve a certain amount of equality over the course of the troubles, which they had previously been denied. Look at things like the civil rights marches. So things were being "achieved", but often by peaceful means.

* Fair few caveats to that, such as Northern Ireland being created, the British Monarch remaining head of state, an oath to be sworn to the monarch on taking office, the treaty ports etc. Overall though they did win the "freedom to achieve freedom".