When are you applying because I think the "Admissions" deadline for the Bachelors taught in English was last week (27th Jan)? Next application period will be in the autumn for entrance in Jan 2017 for some programmes (not all start new programmes in the winter).
Anyway, the eligibility criteria are here:
https://studyinfo.fi/wp2/en/higher-educ ... bachelors/
There is no specific mention of A levels, so I guess they would fall under the category of "completing high school education". It might also depend which programme you are applying for and what subjects you are offering at A level. For example, it seems unlikely that you would be able to get onto an engineering programme without at least an AS level in maths.
I suggest you choose the programmes that you are interested in and then send an email to the UAS asking for more information. Again, the same applies to the language criteria. Usually English is tested at the entrance exam. They might exempt you from that part of the test if you have suitable A levels.
In my experience, there are very very few students at UAS who have applied with A levels, so you might not get an answer on here.