When you are told to discuss someone's criminal liability without any restrictions then you need to consider all of the offences that could be charged.
The first blow seems to have broken both layers of skin so couldn't that be a S18 and/or S20 offence? Assault occasioning ABH is certainly a possible charge for the first blow, I agree there. Could it be a charge for the second blow - what counts as 'actual bodily harm'? Don't forget assault, and battery - both blows could possibly sustain those charges.
The glass is broken and we aren't told who it belongs to - that could be criminal damage as well.
For each offense, go through the usual structure. Identify the elements of actus reus - have they occurred. If the charge is a 'result' offence, discuss causation (not that there is anything much to say on these facts). Then go through the elements of mens rea - are they satisfied? Then go through possible defences. In all honesty there isn't a lot to discuss here apart from intoxication and the definitions of ABH and wounding once you've identified all of the offences that could be charged.