Great question because it demonstrates one of the traps in English for a new speaker. Nathan's answer is a perfectly correct response to the question if we were only looking at it from the point of view of English grammar. BTW, I've also seen it written as Solutions Architecture (but that's verging on the pretentious in my opinion...)
However, the question is raised in the context of an ICT job application or CV and here you have to look a little closer at what is meant by the noun phrase Solution Architecture.
Solution Architecture is both a thing: "I designed the solution architecture for x" and a skill/discipline: "I studied solution architecture as part of my degree"
Looking back at what the OP wants to say and his first example:
I want to say that I've specialties in Web Applications and (plural of) Solution Architecture
I have specialties in Web Applications and Solution Architectures.
I have to admit here that I'm looking at this through the filter of 15 years of reading ICT job applications but the first part of this is a bit weak and a bit vague:
I have specialties in Web Applications
Well, so does my daughter because of the time she spends on Facebook and Instagram
I have specialties in Web (or Web Application) development
is clearer and stronger and is a clue on how to approach the next part - it would be grammatically and semantically correct to say Web Developments but nobody uses it and it would be a giveaway that you are struggling with the language a bit. If you wanted to use the plural form then
I have been responsible for the solution architectures of numerous significant systems
would be quite effective.
Keeping to your brief form though you are probably best to keep to the skills:
I have specialties in Web Application development and Solution Architecture.