This can be found in the Events button top right as the first tab. You get 3 chests every 4 hours and 3 bonus chests daily. You should try to open as many of them as you can every day. These chests contain valuable Skill Medals which are a rare resource for increasing the power of your heroes.
Hero Advancement
This is the easiest one especially once your HQ is 20 or above. You simply chose a hero and click upgrade. At hero level 100 it takes one upgrade to get all 3 chests.
City Building
Use your construction speed ups first to gain as many points as you can. Only complete constructions (open presents) if you run low on speed ups as you want to save completions for VS days 2 and 5. Try not to use universal speed ups unless you are close to getting the last chest.
Unit Progression
You get points for starting and using speed ups but not for completing training. You can complete training before, during, or after.
You should have tiered barracks to maximize points. For example, at HQ 27, have 1 barracks at level 19 that train level 6 troops, 1 barracks level 23 to train level 7 troops, 1 barracks at level 26 to train level 8 troops, and 1 barracks at level 27 to train level 9 troops (I will use these levels for the strategy below).
- prepare beforehand by training troops in all 4 barracks at level 5
- complete all 4 barracks to release the troops
- use the level 19 barracks to promote them all from 5 to 6 rapidly using speed ups
- use the level 23 barracks to promote all the level 6 troops to 7 rapidly using speed ups
- use the level 26 barracks to promote all the level 7 troops to 8 rapidly using speed ups
- use the level 27 barracks to promote all the level 8 troops to 9 rapidly using speed ups
- finally, use all 4 barracks to train new troops to level 5
You will easily get all the AR chests so you can save around 500 level 5 troops each AR for VS day 5. I usually have around 2000 extra un-leveled troops by VS day 5.
Once you have T10, you will need to level your barracks to 23, 26, 29, and 30.
Tech Research
Use research speed ups and complete tech research until you have all 3 chests. Planning ahead by checking when this Arms Race will come up and having your research end close to this time helps. Try not to use universal speed ups unless you are close to getting the last chest.
Drone Boost
Only use Drone Battle Data and Drone Parts when this Arms Race overlaps with VS. Otherwise, run 15 rallies to burn 300 stamina to get your chests. Save your Drone Battle Data and Drone Parts for VS Day 1.