Very straightforward. The Winter Update battle pass is ongoing until March 2023, and it is only a 30 level battle pass that still counts for the achievement. I suggest doing this one if possible, instead of the usual 100 level passes.
Battle passes do not expire per se, but after some time they'll be inaccessible if you don't have "Premium" or credits to spend to keep the pass available. For example, the first two seasons are locked for me as I have no credits (only obtained through microtransactions or via "premium" battle pass) and don't have premium.
At any rate, it's merely a matter of time in order to complete a Battle Pass. Play lots and try and do well, and complete the daily/weekly challenges for an extra boost on top of the match rewards. As of this post, each level requires 1000 XP, and the match XP rewards are as follows:
- Arena Match Complete: 150 XP
- Big Team Battle (BTB) Match Complete: 250 XP
- Featured Match Complete: 200 XP
- Winning Team: 50 XP
- Match MVP: 50 XP
- Top 50% of Team: 50 XP
- Free-For-All placement
- 1st: 150 XP
- 2nd: 100 XP
- 3rd: 50 XP
- 4th: 50 XP
- 5th: 50 XP
The Winning Team, Match MVP, and Top 50% of Team awards will stack for a total of 200 XP.