I'm so sorry that I didn't see this in time anon ;_; I will give you tips and hopefully they will help for next time!!

first of all, I was linked this guide (thank you Nora) which was incredibly helpful. this doc is a general overview of how things work, I'm going to give more direct instructions on what I thought was effective https://docs.google.com/document/u/0/d/1QlKW9Qne04TISkVmaRLC_M_1Hx0OQwdC9gq09Id8j3M/mobilebasic

keep in mind: the guide was written based on the Rutile caulis event, and my tips are written based on the Shino caulis event, so there are some discrepancies from each other in how they work, and there will probably be discrepancies between either of them and how the eventual Murr caulis will work, too. (for example: in the guide, it says you can only explore the tower 3 times per day, but during Shino's caulis, you could explore 6 times, 2 per exploration slot)

tower exploration:
- you get two runs per day for each exploration slot. this is regardless of how much tp or mp you use for that run, so it's best to use the maximum every time! (the exceptions being the first and last days of the events, which are incomplete days, so there aren't 8 hours for those windows, and you should try to do 3 runs within the day to get the daily mission.) be sure to turn the mp boost on!
- the "center" slot as mentioned in the guide is the one at the top that only sends the focus character. if you only have so much tp/time and can't do 6 max tp/mp 4 hour runs, try to prioritize to get longer runs out of the center slot as much as you can
- it doesn't matter which chibis you send for exploration. you have to use different characters but there are no bonuses for using certain characters or for having stronger chibis or anything. follow your heart
- you'll want to do normal training twice and normal battles 3 times a day for the daily event achievements, but if you don't have enough tp/mp to work with and have to pick between daily achievements or longer runs in the exploration tower, prioritize the exploration tower

trial doors:
- there are four doors: a wooden one, a silver one, a gold one, and a special crystal one with limited access. these had to be unlocked in order: you have to go through the wooden door first to get access to the silver door, then you had to go through the silver door to get access to the gold door, then you had to go through the gold door to get access to the crystal door.
- during Shino caulis, there was ONLY a chance of Shino dropping in the gold door. use 300 keys (the minimum) to clear the wooden and silver doors, then focus on the gold door exclusively until the card drops. after the card drops once, it's removed from the rewards pool. the card is NOT in the reward pool for the crystal door. if you look at this screen, as shown in the guide, at the part where it's labeled 'potential drops,' it should show a thumbnail of the card if you're at the right door. (you can also click on the "..." button here to see what other drops you might get at the end of a run.) https://lh7-us.googleusercontent.com/docsz/AD_4nXdMpdubFpFBATqXe7B_ywxl-ixzc35XHXG8WoEaDr0p840TM4KWtxq4e5zM-8tIkNt0OvcReLILEEPEMeKtwK2KfsMZXE1pfIs_cLsgxSt8up00SyBNnEz28l873SDhkgsh2_R0swP6-u-0Zky_pAgcxMNr=s800?key=cFBaau79Y9apJZfTZEjJvg
- the crystal door is limited to either two 300 key runs or a single 600 key run per day. it has a higher payout of point rewards for climbing the ladder if you want to get to 2mil for the card in the ladder reward. however, if you don't think you'll make it to the 2mil mark regardless, you should just save your keys for the gold door.
- in the guide, it says that if your party wipes during the trial door fights, you can use mp to revive, but during Shino caulis, you had to spend one mana stone to revive your party. personally I was fine with spending mana stones because the reward ladder was giving me more mana stones than I spent. however, especially if your team is on the weaker side, using more keys per run means fewer opportunities to wipe and have to use mana stones, so go for 1500 key runs (or even 3000 key runs later if you still haven't gotten the card drop) as much as you can.
- like with most event bonuses, you want to run event cards in your party during training and get a chibi with an event bonus percentage and include that chibi in your trial door team. you only need one event bonus chibi, but the bonus can be attached to any chibi from any chara, not just the event chibi

making a strong chibi team for the trial doors that doesn't die as much:
- in the caulis trial doors, a chibi's HP stat is determined by its stat total, while its ATK stat is determined by its score. this Shino chibi's score is 34228 https://pbs.twimg.com/media/ErdRNPVU0AYcStX?format=jpg&name=large
- a chibi's score is mostly determined by the number of traits it has. I took that Shino chibi cap from this guide on how to get more traits and thus a higher scoring chibi https://twitter.com/izayoi__seeing/status/1348635903690870784
- because HP is still determined by stats, rather than following the above guide exactly, build a team that has a higher ratio of daiseikou cards as usual. if possible, include cards that have BOTH a daiseikou skill and a trait drop skill. Valentine's Faust and north ballad Mithra are cards with both, for example
- list of cards with daiseikou skills https://mahoyaku.fandom.com/wiki/Card_Skill/Training_Success
- list of cards with increased trait drop chance skills https://mahoyaku.fandom.com/wiki/Card_Skill/Traits#All_Stats

navigating trial door tiles:
- I specifically made this section to tell you that when you hit the magical beast's blessing tile, you should pick the blue icon with the picture of a key as much as possible to equip it and and level it up. this effect refunds some of the keys you spent at the end of your run. the icon can be seen here at the bottom right https://lh7-us.googleusercontent.com/docsz/AD_4nXdGoi8Uw2FtD0hgaqK4G7dMgnVIS1l5IHlwhEog5Q4H5VM7dVTRgM34oovaDH3dDE55IUrfoTJ-IMGYYlENwhBVQvTj7KT4oeXtE933e0GKVgxeF_CFdPhriPMYCOuYimjW8VpCBtCFA_gqtnAMbHCYNPW3=s800?key=cFBaau79Y9apJZfTZEjJvg
- look ahead and try to plan your route out a little in advance so you don't get stuck in a weird place away from the heal tiles. it's best to mostly focus on the 50% heal tiles and the skill tiles. there's no real hierarchy of which skill tiles are best that I can tell, all of them are good
- I don't actually know if getting chests increases your chances of getting the reward card to drop, but I hit chests as much as I could just in case.

bonding/fureai/rapport:
- BOND WITH YOUR CUTE MONSTER FRIEND LOTS
- during the regular bonding activities, sometimes keys will drop. bond with your cute monster friend lots
- if you bond with them even after your bond is maxed out (maxes out at 100), bonding activities may still drop keys, so keep bonding
- feeding bonds faster, but doesn't drop keys, so after your bond is maxed, there's no need to keep doing it anymore