There’s a very particular take in Galatians on fighting sin and growing in godliness which is worth noting, firstly in our own lives and secondly in our preaching and pastoring. It emerges towards the end of the letter. Paul sets out the contrasting ‘acts of the flesh’ (5.19-21a) and ‘fruit of the Spirit’ (5.22-23a). But he does not (we must note!) directly command or exhort the Galatians to fight against sin or to work directly at growth in godly characteristics. He does both of those things elsewhere – respectively in, for example, Col 3.5-10 and 2 Pet 1.5-8 – but not here in Galatians. Mortification of sin is biblical teaching, but not Galatian, I think.
What is Paul doing in Galatians with regard to godliness, then? ‘So I say, live by the Spirit, and you will not gratify the desires of the flesh’ (5.16). Here is a command – live by the Spirit – and a statement of a consequence that will follow if we obey that command – it will then turn out that we are in fact not gratifying the desires of the flesh.
So the crucial godliness question in Galatians is, what does it means to ‘live by the Spirit’?
Two answers stand out:
i) In the immediate context, Paul has commanded them to ‘serve one another humbly in love’, because this fulfils the entire law (5.13b-14). The subsequent command to ‘live by the Spirit’ (v.16) looks rather like a restatement of this. Thus to live by the Spirit is to live a life of humble, loving service towards others.
ii) In the wider Galatian context, living by the Spirit means not relying on law-keeping for security in right-standing with God: ‘Are you so foolish? After beginning by means of the Spirit, are you now trying to finish by means of the flesh?’ (3.3).

Put this together, and it looks like this:
We must keep striving to find our entire security in our right-standing with the Lord not in any law-like list of achievements, but only in the works that the Spirit brings about in us. We must strive, too, to make humble, loving service of others the distinguishing feature of our attitudes and actions. (And note that these two have a natural link: if I get my sense of secure right-standing with the Lord through any list of laws I have kept, I will inevitably compare myself favourably with others in order to make my list of well-kept laws seem impressive enough – and that is the very antithesis of a loving, humble, servant heart.)
As we are focused on these two strivings – for the right foundation of our justification, for the right fundamental attitude to others – we will discover (back now to 5.16) that we are not gratifying (fuelling, feeding, stroking, pleasing) the desires of the flesh.
There is more than one way prescribed in Scripture for fighting particular sins, and we need all of them. One is to assault them directly. Another, as set out in Galatians, is to focus Christ and the Spirit, not law, as the basis for our secure standing with God, and to co-operate with the Spirit’s work in developing in us a life of humble, loving service.