What part? Dublin is more expensive than other cities, but it's possible to find greater variety of cheaper stuff there. You can shop in Spar, rent in somewhere like Ranelagh and yes it will be substantially higher than living costs in the UK. Things like milk cost €1.12, cheese €2.59 cereals €2-4...I can't think of good solid examples really. It's extremely possible to cut down your living costs without living off pot noodles. The main supermarkets are Dunnes and Tesco (Tesco is more expensive here by about 15% than in the UK). There's M&S too, but we don't have Morrisons, Asda, Sainsburys or Waitrose. We do have Lidl and Aldi, and a smaller supermarket that's not a discount called Supervalu. All supermarkets do loads of promos and offers, and Lidl and Aldi obviously is where you can pick up staples much cheaper. If you go to tesco all the time, your moey will evaporate.
The cheapest rent I have heard of is about €400 a month. Trinity Hall costs €6-9k a year, you can get much cheaper than that but Halls has the instant community of mostly non-Irish students bonus. Places with a D2, D4 and D6 postcode are best avoided, extremely expensive. There are old fashioned suburbs practically in the city centre with pretty low rents. They have the rep of being working-class areas, but there's little to no scumbag element. These include Cabra and Phibsboro. Further out there's Fairview, Marino, Whitechurch, Santry and Drumcondra. Both Luas lines (tram) run to the Southside, which doesn't have great scope for cheap non-dangerous accommodation. The trains are pretty good (much cheaper than UK trains) and there's loads of bus routes that are really regular. The standard bus fare is €1.65, you can get student bus tickets but you won't save much if your bus fare is low.
www.daft.ie Have a look here, main renting website. Don't be alarmed by ridiculous prices for new apartments- have a look at some of the places I mentioned- look out for postcodes D1, D3, D5, D7, D9, D11....they're your best bet without being too far away. The best deals are posted up on noticeboards on campus, really cheap.
Shopping- try not to, do it when you're in the UK. This is the biggest rip-off. Topshop I'll give as an example. All shoes that cost £65 in the UK cost €99 here, even though the actual conversion allowing for higher wages and costs here would be roughly €74. Jeans cost £40 but €61 here- again actual conversion €45. They are the worst offenders, but there's a good few others out there. We do have Penneys (Primark in the UK, but it's originally Irish and the ones in the city are brilliant), Dunnes (slightly more expensive than Penneys), H&M and Forever 21. Almost all high-street UK shops are here, with the exception of Uniqlo, I know we don't have that. Can't think of others.
Pints do cost €5-6 here, and spirit+mixer will cost €6-9. There are deals everywhere though, in particular in clubs aimed at students. Some deals consist of a bunch of drinks for €10, or free drinks before 11 but most are all drinks €3/3.50. They can't lower them to the prices offered in the UK, they're protected fiercely and if promotions clearly aim to get everyone hammered they get shut down. For the same reason- you can't buy alcohol in any off-license after 10pm and all clubs close at 2.30AM (except 2- D2 and Coppers) which as you can imagine is a brilliant idea- everyone is on the streets at the same time, without the benefit of longer to let the drink soak in. What a lot of people do is pre-drink. There's always great deals on cans if they're your thing and naggins generally cost €7.50. If you're smart about it you can have a cheap night. Other people bring drink in with them to clubs, as none of them search anymore. Night bus home costs €5, taxis are fairly reasonable also.
So see how that compares? If you want to know anything else I can probably answer it..