Making a hand of = making fun of/poking fun at (Never heard this; I regularly hear ' to slag someone' is to tease them.)
Going on with = teasing (i.e., “don’t be going on with her”) (Never heard this either)
Give over = stop it ( I have heard this, but not very often. I have frequently heard 'cut it out')
Glad of it = glad (I have heard this, but not very often)
Handle your feet well = dance (I don't think I have heard this)
Give hard with the tongue = scold (i.e., “Mam’s going to give you hard with her tongue.”) (I have never heard this)
Amplush = mess (I have never heard this)
Upon my life= I swear (I have heard this, but not sure it was in Ireland. Much more likely to hear 'I swear to God' or perhaps with someone younger 'Cross my heart, hope to die'. Sounds a little ominous, I know)
Go off on = get mad (I have heard 'to go off on
one' as in 'he really went off on one')
My guess is that different phrases are common in different parts of the country. There are probably some pretty standard ones and others that are quite localised. Now where have I heard that kind of thing before......!

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Is foghlaimeoir mé. I am a learner. DEFINITELY wait for others to confirm and/or improve.
Beatha teanga í a labhairt.